An element a of a ring R is called Drazin invertible if there exists b∈R such that ab =ba,bab =b,and a -a2 b is nilpotent.The element b above is unique if it exists and is denoted as aD .The equivalent conditions of ...An element a of a ring R is called Drazin invertible if there exists b∈R such that ab =ba,bab =b,and a -a2 b is nilpotent.The element b above is unique if it exists and is denoted as aD .The equivalent conditions of the Drazin inverse involving idempotents in R are established.As applications, some formulae for the Drazin inverse of the difference and the product of idempotents in a ring are given.Hence,a number of results of bounded linear operators in Banach spaces are extended to the ring case.展开更多
Two constructions of Cartesian authentication codes form involutory and idempotent matrices over finitefields are presented and their size Parameters are computed. Moreover, assume that the encoding rules are chosen a...Two constructions of Cartesian authentication codes form involutory and idempotent matrices over finitefields are presented and their size Parameters are computed. Moreover, assume that the encoding rules are chosen ac-cording to a uniform Probablity distribution, the PI and Ps which dend the largest Probablities of a successful impersonation attack and a successful substitution attack respectively of these codes are also computed. Finially, it is Provedthat thase two Cartesian authentication codes are isomorphic.展开更多
This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.
For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all gen...For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.展开更多
In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probab...In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.展开更多
On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and cont...On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].展开更多
A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has...A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has many interesting properties and contains the classes of n-*-paranormal operators and quasi-*-paranormal operators. The aim of this note is to show that every Riesz idempotent E;with respect to a non-zero isolated spectral point λ of an（n, k）-quasi-*-paranormal operator T is self-adjoint and satisfies ran E;= ker（T- λ） = ker（T- λ）*.展开更多
A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) o...A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.展开更多
In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive fo...In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.展开更多
In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive for...In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.展开更多
In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinator...In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.展开更多
<span style="font-family:Verdana;">Let <img alt="" src="Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png" />be the partial symmetric semigroup on <img alt="" src=&qu...<span style="font-family:Verdana;">Let <img alt="" src="Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png" />be the partial symmetric semigroup on <img alt="" src="Edit_86c31e58-0588-44fc-8ff3-78c73dc14be6.png" />and let <img alt="" src="Edit_09f7ec2a-49d1-463d-952e-93fbe00740cd.png" />and <img alt="" src="Edit_4aca07c1-9a36-44b6-83af-46fdd6278ca4.png" />be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of <img alt="" src="Edit_72d2bbdf-2b96-4812-a993-f49640bb98c9.png" />, respectively. In this paper we investigate the cardinalities of <img alt="" src="Edit_95038cdc-5496-495f-bfb9-29c817ba2df4.png" />and <img alt="" src="Edit_f8d3d782-ff8c-43b3-84af-d21a3f4291d5.png" />, the set idempotents of <img alt="" src="Edit_ac8237f8-83ec-4767-9029-b546377bf106.png" />and <img alt="" src="Edit_8b1bf8bf-7472-453c-965d-7308da5b4f4c.png" />, respectively. We also investigate the cardinalities of certain equivalences on <img alt="" src="Edit_e5f7aec4-67c1-48ba-8d03-ea6ceb2e7627.png" />and <img alt="" src="Edit_42a31943-fe9d-4ea8-8999-3aadb705fb38.png" />.</span>展开更多
基金The National Natural Science Foundation of China(No.11371089)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)+2 种基金the Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX13-072)the Scientific Research Foundation of Graduate School of Southeast Universitythe Fundamental Research Funds for the Central Universities(No.22420135011)
文摘An element a of a ring R is called Drazin invertible if there exists b∈R such that ab =ba,bab =b,and a -a2 b is nilpotent.The element b above is unique if it exists and is denoted as aD .The equivalent conditions of the Drazin inverse involving idempotents in R are established.As applications, some formulae for the Drazin inverse of the difference and the product of idempotents in a ring are given.Hence,a number of results of bounded linear operators in Banach spaces are extended to the ring case.
文摘Two constructions of Cartesian authentication codes form involutory and idempotent matrices over finitefields are presented and their size Parameters are computed. Moreover, assume that the encoding rules are chosen ac-cording to a uniform Probablity distribution, the PI and Ps which dend the largest Probablities of a successful impersonation attack and a successful substitution attack respectively of these codes are also computed. Finially, it is Provedthat thase two Cartesian authentication codes are isomorphic.
基金supported by the National Natural Science Foundation of China under grant No.11171222the Doctoral Program of the Ministry of Education under grant No.20094407120001
文摘This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.
文摘For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.
基金Foundation item:The Key Project(03060)of Chinese Ministry of Education.
文摘In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.
文摘On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].
基金supported by National Natural Science Foundation of China(11301077,11301078,11401097,11501108)Natural Science Foundation of Fujian Province(2015J01579,2016J05001)
文摘A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has many interesting properties and contains the classes of n-*-paranormal operators and quasi-*-paranormal operators. The aim of this note is to show that every Riesz idempotent E;with respect to a non-zero isolated spectral point λ of an（n, k）-quasi-*-paranormal operator T is self-adjoint and satisfies ran E;= ker（T- λ） = ker（T- λ）*.
基金Supported by NSFC grant No. 10371002 (Y. Chang) and No.19901008 (J. Lei)
文摘A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.
文摘In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.
文摘In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.
文摘In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.
文摘<span style="font-family:Verdana;">Let <img alt="" src="Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png" />be the partial symmetric semigroup on <img alt="" src="Edit_86c31e58-0588-44fc-8ff3-78c73dc14be6.png" />and let <img alt="" src="Edit_09f7ec2a-49d1-463d-952e-93fbe00740cd.png" />and <img alt="" src="Edit_4aca07c1-9a36-44b6-83af-46fdd6278ca4.png" />be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of <img alt="" src="Edit_72d2bbdf-2b96-4812-a993-f49640bb98c9.png" />, respectively. In this paper we investigate the cardinalities of <img alt="" src="Edit_95038cdc-5496-495f-bfb9-29c817ba2df4.png" />and <img alt="" src="Edit_f8d3d782-ff8c-43b3-84af-d21a3f4291d5.png" />, the set idempotents of <img alt="" src="Edit_ac8237f8-83ec-4767-9029-b546377bf106.png" />and <img alt="" src="Edit_8b1bf8bf-7472-453c-965d-7308da5b4f4c.png" />, respectively. We also investigate the cardinalities of certain equivalences on <img alt="" src="Edit_e5f7aec4-67c1-48ba-8d03-ea6ceb2e7627.png" />and <img alt="" src="Edit_42a31943-fe9d-4ea8-8999-3aadb705fb38.png" />.</span>
