Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrice...Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.展开更多
In this paper, we discussed the property of rectangular band semiring congruence and ring congruence on a semiring and gave some characterizations and structure of rectangular ring congruence on an E-inversive semiring.
This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplicat...This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplication operator semigroup of semiring semigroup.展开更多
Let M be a finitely generated free semimodule over a semiring S with identity having invariant basis number property with a basisα={α1,...,αk}.The complement■of the reduced non-zero component graph■of M,is the si...Let M be a finitely generated free semimodule over a semiring S with identity having invariant basis number property with a basisα={α1,...,αk}.The complement■of the reduced non-zero component graph■of M,is the simple undirected graph with■as the vertex set and such that there is an edge between two distinct vertices■and■if and only if there exists no i such that both ai,biare non-zero.In this paper,we show that the graph■is connected and find its domination number,clique number and chromatic number.In the case of finite semirings,we determine the degree of each vertex,order,size,vertex connectivity and girth of■.Also,we give a necessary and sufficient condition for■to be Eulerian or Hamiltonian or planar.展开更多
文摘Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.
基金Supported by the National Natural Science Foundation of China(10961014,11101354) Supported by the Natural Science Foundation of Jiangxi Province(0611051) Supported by the Science Foundation of the Education Department of Jiangxi Province(GJ 09459)
文摘In this paper, we discussed the property of rectangular band semiring congruence and ring congruence on a semiring and gave some characterizations and structure of rectangular ring congruence on an E-inversive semiring.
文摘This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplication operator semigroup of semiring semigroup.
基金supported by CSIR Emeritus Scientist Scheme(21(1123)/20/EMR-II)of Council of Scientific and Industrial Researchthis research is also supported by Dr.M.G.R.Research Scholarship by Manonmaniam Sundaranar University。
文摘Let M be a finitely generated free semimodule over a semiring S with identity having invariant basis number property with a basisα={α1,...,αk}.The complement■of the reduced non-zero component graph■of M,is the simple undirected graph with■as the vertex set and such that there is an edge between two distinct vertices■and■if and only if there exists no i such that both ai,biare non-zero.In this paper,we show that the graph■is connected and find its domination number,clique number and chromatic number.In the case of finite semirings,we determine the degree of each vertex,order,size,vertex connectivity and girth of■.Also,we give a necessary and sufficient condition for■to be Eulerian or Hamiltonian or planar.