In this paper, we investigate the investigate the Morita characterizaton of projective free rings,and show that projective free rings have Mortita invariant properties.
We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of...We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring Mn（R） is weakly nil-clean, and to show that the endomorphism ring EndD（V） over a vector space VD is weakly nil-clean if and only if it is nil-clean or dim（V） = 1 with D Z3.展开更多
For a prime p,let E_（p,p^m）={（a p^（m-1） b d）｜a,b,c∈Z_p,d∈Z_（p^m）}. We first establish a ring isomorphism from Z_（p,p^m） onto E_（p,p^m）. Then we provide a way to compute-d and d^（-1） by using arithmeti...For a prime p,let E_（p,p^m）={（a p^（m-1） b d）｜a,b,c∈Z_p,d∈Z_（p^m）}. We first establish a ring isomorphism from Z_（p,p^m） onto E_（p,p^m）. Then we provide a way to compute-d and d^（-1） by using arithmetic in Z_p and Z_（p^m）, and characterize the invertible elements of E_（p,p^m）. Moreover, we introduce the minimal polynomial for each element in E_（p,p^m） and give its applications.展开更多
Considered in this paper are pseudo-injective modules and principally pseudoinjective modules, which are generalizations of quasi-injective modules and PQ-injective modules. Pseudo-injective modules are dual to pseudo...Considered in this paper are pseudo-injective modules and principally pseudoinjective modules, which are generalizations of quasi-injective modules and PQ-injective modules. Pseudo-injective modules are dual to pseudo-projective modules. We study their properties and endomorphism rings, and obtain some properties of the Jacobson radical of such rings.展开更多
Let (?, ?) be a linear matrix problem induced from a finite dimensional algebra ∧. Then an? ×? matrix M in R(?, ?) is indecomposable if and only if the number of links in the canonical formM (∞) of M is equal t...Let (?, ?) be a linear matrix problem induced from a finite dimensional algebra ∧. Then an? ×? matrix M in R(?, ?) is indecomposable if and only if the number of links in the canonical formM (∞) of M is equal to. ?-dim? ? 1. On the other hand, the dimension of the endomorphism ring of M is equal to ?-dim? ? σ(M).展开更多
In this paper,we give the equivalent characterizations of principally quasi-Baer modules,and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually ...In this paper,we give the equivalent characterizations of principally quasi-Baer modules,and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually subisomorphic principally quasi-Baer modules is also principally quasi-Baer.Moreover,we prove that left principally quasi-Baer rings have Morita invariant property.Connections between Richart modules and principally quasi-Baer modules are investigated.展开更多
文摘In this paper, we investigate the investigate the Morita characterizaton of projective free rings,and show that projective free rings have Mortita invariant properties.
文摘We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring Mn（R） is weakly nil-clean, and to show that the endomorphism ring EndD（V） over a vector space VD is weakly nil-clean if and only if it is nil-clean or dim（V） = 1 with D Z3.
基金Supported by the Research Project of Hubei Polytechnic University(17xjz03A)
文摘For a prime p,let E_（p,p^m）={（a p^（m-1） b d）｜a,b,c∈Z_p,d∈Z_（p^m）}. We first establish a ring isomorphism from Z_（p,p^m） onto E_（p,p^m）. Then we provide a way to compute-d and d^（-1） by using arithmetic in Z_p and Z_（p^m）, and characterize the invertible elements of E_（p,p^m）. Moreover, we introduce the minimal polynomial for each element in E_（p,p^m） and give its applications.
基金the National Natural Science Foundation of China (10371101).
文摘Considered in this paper are pseudo-injective modules and principally pseudoinjective modules, which are generalizations of quasi-injective modules and PQ-injective modules. Pseudo-injective modules are dual to pseudo-projective modules. We study their properties and endomorphism rings, and obtain some properties of the Jacobson radical of such rings.
基金the National Natural Science Foundation of China (Grant No. 19831070) and the Doctoral Foundation of Institution of Higher Education.
文摘Let (?, ?) be a linear matrix problem induced from a finite dimensional algebra ∧. Then an? ×? matrix M in R(?, ?) is indecomposable if and only if the number of links in the canonical formM (∞) of M is equal to. ?-dim? ? 1. On the other hand, the dimension of the endomorphism ring of M is equal to ?-dim? ? σ(M).
基金Foundation item： the National Natural Science Foundation of China （No. 10671122）.
文摘In this paper,we give the equivalent characterizations of principally quasi-Baer modules,and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually subisomorphic principally quasi-Baer modules is also principally quasi-Baer.Moreover,we prove that left principally quasi-Baer rings have Morita invariant property.Connections between Richart modules and principally quasi-Baer modules are investigated.
