張理江 石定琴
摘? 要:該文在給定的半模M上定義了上三角矩陣半環(huán)U2(R,M),并利用環(huán)論的方法研究了它的相關(guān)性質(zhì),得到半環(huán)U2(R,M)是加法冪等的充分必要條件是模R是加法冪等的,半環(huán)U2(R,M)是零和自由的充分必要條件是半環(huán)R和半模模M都是零和自由的,以及其子半環(huán)的特征。在同構(gòu)意義下,得到任何半環(huán)R都可以自然嵌入到半環(huán)U2(R,M)中。
關(guān)鍵詞:半環(huán)? ?半模? ?子半環(huán)? ?同構(gòu)
中圖分類號:O153.3? ? ? ? ? ? ? ? ? ? ? ? 文獻(xiàn)標(biāo)識碼:A文章編號:1672-3791(2021)07(b)-0193-03
Upper Triangular Matrix Semiring U2(R,M)
ZHANG Lijiang? SHI Dingqin
(College of Science, Jiujiang University, Jiujiang, Jiangxi Province, 332005? China)
Abstract: In this paper, the author defines the semiring U2(R,M) on the basis of the semi-module M, and studies its related properties on the method of ring theory, gets the necessary and sufficient condition that semiring U2(R,M) is additive idempotent is that the semiring R is additive idempotent, and necessary and sufficient conditions for a semiring U2(R,M) to be additive idempotent, zero sum free, and the characteristics of its sub semirings are obtained. In the sense of isomorphism, it is obtained that any semiring R can be naturally embedded in semirings U2(R,M).
Key Words: Semiring; Semimodule; Subsemiring; Isomorphism
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