共查询到20条相似文献,搜索用时 46 毫秒
1.
M. A. Lukin 《Russian Mathematics (Iz VUZ)》2008,52(12):65-68
We describe the structure of semirings which are unions of a ring and a half-body. 相似文献
2.
3.
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. 相似文献
4.
5.
6.
7.
利用同余关系把粗糙集理论引入到半环里,给出了半环中的一个子集的上,下近似的概念,并研究了其一系列性质;另外我们还讨论了半环中的粗糙理想及性质. 相似文献
8.
9.
满足a+ab=a+b的幂等半环的结构 总被引:1,自引:0,他引:1
本文讨论了满足a+ab=a+b的幂等半环的结构,给出这种幂等半环是左零半环的伪强右正规幂等半环,并得出这种幂等半环与环的直积是左环的伪强右正规幂等半环. 相似文献
10.
Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR(ω) ∞ implies G-dimω(M) ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω(M) is finite. 相似文献
11.
Yaroslav Shitov 《Linear and Multilinear Algebra》2013,61(1):201-220
The two common concepts of singularity for matrices over semirings are being studied since the 1970’s and arise from natural generalizations of the determinant and linear dependence. They were introduced in the context of schedule algebras by Gondran and Minoux, who proved later that the concepts discussed are equivalent over any selective invertible semiring. We present an approach that uses a generalization of power series arithmetic and, in particular, allows to derive a short proof for the theorem of Gondran and Minoux. Our main result is a complete concise characterization of semirings over which the two concepts of singularity are equivalent. 相似文献
12.
The lattice of idempotent distributive semiring varieties 总被引:7,自引:0,他引:7
A solution is given for the word problem for free idempotent distributive semirings. Using this solution the latticeL (ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out thatL (ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four
copies of the latticeL(B) of all band varieties. ThereforeL(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.
Project supported by the National Natural Science Foundation of China (Grant No. 19761004) and the Provincial Applied Fundamental
Research Foundation of Yunnan (96a001z). 相似文献
13.
半环R被称为实半环,若对于任意的n∈N,方程x1^2+…+xn^2=0在R中只有零解:x1=…=xn=0.为了刻画实半环,引入了实理想和极小素理想的概念,利用同余的方法,得到了可减半环类中实半环的结构定理. 相似文献
14.
Xiaoyan Yang 《代数通讯》2013,41(1):131-142
In this article, FP-injective complexes are introduced and studied. We prove that (⊥??, ??) is a hereditary cotorsion theory if and only if R is a left coherent ring, where ?? denotes the class of all FP-injective complexes of left R-modules. Simultaneously, we study the existence of FP-injective preenvelopes and FP-injective covers. 相似文献
15.
Igor Dolinka 《Algebra Universalis》2009,60(1):19-35
We give a sufficient condition which ensures that a semiring with an idempotent addition is inherently nonfinitely based.
This enables us to provide a number of small and natural examples of nonfinitely based semirings, including semirings of binary
relations on a finite set.
Supported by Grant No.144011 of the Ministry of Science of the Republic of Serbia. 相似文献
16.
François Couchot 《代数通讯》2013,41(1):381-389
It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2. This implies that the projective dimension of any countably generated FP-injective module over an Archimedean chain ring is less or equal to 3. 相似文献
17.
半环半直积的同构定理 总被引:1,自引:0,他引:1
谢蓓蓓 《纯粹数学与应用数学》2004,20(4):364-367
半群半直积及封闭性刻划于文[1],为将半直积的研究推广至半环中,本文首先在交换半环与交换半群的直积上定义加法及乘法运算,从而构造了一类半环;半环半直积.并讨论了半环半直积的同构等问题. 相似文献
18.
Necessary and sufficient conditions for the regularity of complete matrix semirings over an arbitrary semiring are obtained. 相似文献
19.
20.
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of invertible matrices. 相似文献