謝祥云，谷澤

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關(guān)于序半群的正則和反強(qiáng)正則同余

謝祥云，谷澤

（五邑大學(xué) 數(shù)學(xué)與計算科學(xué)學(xué)院，廣東 江門 529020）

引入了序半群中反擬鏈和反強(qiáng)正則同余等概念，討論了它們的一些性質(zhì)，給出了正則同余和反強(qiáng)正則同余的一般刻畫.

反擬鏈；反強(qiáng)正則同余；正則同余

1 引言與預(yù)備知識

本文用到的其他定義和術(shù)語參見文獻(xiàn)[12-13].

2 正則和反強(qiáng)正則同余

由性質(zhì)1，有推論1.

.

3 正則和反強(qiáng)正則同余的刻畫

為給出正則和反強(qiáng)正則同余的一般刻畫，先給出定義3.

證明 1）、2）容易證明，我們僅證明3）.

我們僅證A），用同樣的方法可證B）、C）、D）.

充分性的證明與必要性類似，證略.

證明 必要性.由引理1及定義2，顯然.

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On Inverse Strongly Regular Congruences on Ordered Semigroups

XIEXiang-yun, GUZe

(School of Mathematics and Computation Science, Wuyi University, Jiangmen 529020, China)

In this paper, inverse quasi-chain and inverse strongly regular congruences on ordered semigroups are introduced. Some of their properties are studied, and some theorems are given to characterize regular congruences and inverse strongly regular congruences.

inverse quasi-chain; inverse strongly regular congruences; regular congruences

1006-7302（2012）01-0001-05

O152. 7

A

2011-07-26

國家自然科學(xué)基金資助項(xiàng)目（No.10961014）；廣東省科技計劃資助項(xiàng)目（2010B010600039）；廣東省自然科學(xué)基金資助項(xiàng)目（S201101000368）

謝祥云（1964—），男，安徽舒城人，教授，博士，碩士生導(dǎo)師，研究方向?yàn)樾虬肴旱拇鷶?shù)理論、模糊代數(shù)、粗糙集理論.