加法可换可消半环的一个结构定理及应用

半环是一种有很好实际背景和应用前景的代数结构,尤其对于计算机语言的研究有极为重要的作用。因此,对半环的研究越来越引起人们的关注。本文首先证明了每个加法可换可消半环有一个包环,然后在此基础上证明了它们是多重线性等价的,最后证明了加法可消的交换半坏上的Levitzki-Amitsur定理。     

G-Prime Ideals in Semirings and Their Skew Group Semirings

Semirings have been studied by various researchers either in an attempt to broaden the techniques coming from semigroup theory or generalization of group theory and ring theory. From an algebraic point of view, semirings provide the most natural generalization of the theory of rings. In this article, we generalize some of the results of Lorenz and Passman (1979 Lorenz , M. , Passman , D. S. ( 1979 ). Prime ideals in crossed products of finite groups . Israel J. Math. 33 ( 2 ): 89 – 132 .[Crossref], [Web of Science ®] , [Google Scholar]) for semirings with finite group action on them.     

Frobenius and Dieudonné theorems over semirings

We obtain semiring versions of classical theorems by Frobenius and Dieudonné on determinant, singularity, and non-singularity preservers.     

Semicorings and Semicomodules

In this paper, we introduce and investigate semicorings over associative semirings and their categories of semicomodules. Our results generalize old and recent ones on corings over rings and their categories of comodules. The generalization is not straightforward and even subtle at several places due to the nature of the base category of commutative monoids which is neither Abelian (not even additive) nor homological, and has no nonzero injective objects. To overcome these and other difficulties, a combination of methods and techniques from categorical, homological and universal algebra is used including a new notion of exact sequences of semimodules over semirings.     

链式条件下的半环的(∈,∈∨q(λ,μ))-模糊双理想

给出双诺特半环、双阿丁半环的概念。通过使用半环的双理想族建立半环的(∈,∈∨q(λ,μ))-模糊双理想。利用(∈,∈∨q(λ,μ))-模糊双理想刻画双诺特半环、双阿丁半环。     

Maps preserving scrambling index

In this paper we characterize bijective linear maps on matrices over semirings that preserve scrambling index.     

幺半环上几类模糊自动机的关系

给出了幺半环上非确定的模糊自动机和确定的模糊自动机及其语言的定义,证明了幺半环上三类非确定的模糊自动机间的等价性和三类确定的模糊自动机间的等价性,讨论了幺半环上三类非确定的模糊自动机和第四类非确定的模糊自动机之间的关系,以及幺半环上非确定的模糊自动机和确定的模糊自动机之间的关系.