| On Ordered Ideals in Ordered Semirings |
| Received:July 05, 2010 Revised:January 12, 2011 |
| Key Words:
ordered semiring ordered ideal simple semiring minimal ideal matrix.
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| Fund Project:Supported by the National Natural Science Foundation of Jiangxi Province (Grant No.2010GZS0093). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.06.004 |
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