On Ordered Ideals in Ordered Semirings

DOI：10.3770/j.issn:1000-341X.2011.06.004

 作者 单位 甘爱萍 江西师范大学数学与信息科学学院, 江西 南昌 330022 姜样兰 江西警察学院, 江西 南昌 330103

本文引入了序半环,序半环的序理想,极小和极大理想,以及单序半环等概念;研究了它们的一些性质,并对极小理想进行了刻划.另外,本文也考虑了序半环上的矩阵半环.本文的部分结论与序半群,半环上的矩阵半环上的相关结论类似.

An ordered semiring is a semiring $S$ equipped with a partial order $\leq$ such that the operations are monotonic and constant 0 is the least element of $S$. In this paper, several notions, for example, ordered ideal, minimal ideal, and maximal ideal of an ordered semiring, simple ordered semirings, etc., are introduced. Some properties of them are given and characterizations for minimal ideals are established. Also, the matrix semiring over an ordered semiring is considered. Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups, and on the matrix semiring over a semiring.