In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of s...In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.展开更多
A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. It is said that a ring R is a JB-ring provided that R/J（R） is a QB-ring, where J（R） is th...A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. It is said that a ring R is a JB-ring provided that R/J（R） is a QB-ring, where J（R） is the Jacobson radical of R. In this paper, various necessary and sufficient conditions, under which a ring is a JB-ring, are established. It is proved that JB-rings can be characterized by pseudo-similarity. Furthermore, the author proves that R is a JB-ring iff so is R/J（R）^2.展开更多
In this paper, we introduce Green＇s .-relations on semirings and define [left, right] adequate semirings to explore additively non-regular semirings. We characterize the semirings which are strong b-lattices of [left...In this paper, we introduce Green＇s .-relations on semirings and define [left, right] adequate semirings to explore additively non-regular semirings. We characterize the semirings which are strong b-lattices of [left, right] skew-halfrings. Also, as further generalization, the semirings are described which are subdirect products of an additively commutative idempotent semiring and a [left, right] skew-halfring. We extend results of constructions of generalized Clifford semirings （given by M. K. Sen, S. K. MaRy, K. P. Shum, 2005） and the semirings which are subdirect products of a distributive lattice and a ring （given by S. Ghosh, 1999） to additively non-regular semirings.展开更多
文摘In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.
文摘A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. It is said that a ring R is a JB-ring provided that R/J（R） is a QB-ring, where J（R） is the Jacobson radical of R. In this paper, various necessary and sufficient conditions, under which a ring is a JB-ring, are established. It is proved that JB-rings can be characterized by pseudo-similarity. Furthermore, the author proves that R is a JB-ring iff so is R/J（R）^2.
基金Supported by the Natural Science Foundation of Hunan Province (Grant No04JJ4001)the Scientific Research Foundation of Hunan Education Department (Grant No05A014)
文摘In this paper, we introduce Green＇s .-relations on semirings and define [left, right] adequate semirings to explore additively non-regular semirings. We characterize the semirings which are strong b-lattices of [left, right] skew-halfrings. Also, as further generalization, the semirings are described which are subdirect products of an additively commutative idempotent semiring and a [left, right] skew-halfring. We extend results of constructions of generalized Clifford semirings （given by M. K. Sen, S. K. MaRy, K. P. Shum, 2005） and the semirings which are subdirect products of a distributive lattice and a ring （given by S. Ghosh, 1999） to additively non-regular semirings.
