秦官偉,任苗苗,邵勇

(西北大學(xué)數(shù)學(xué)系,陜西 西安 710127)

關(guān)于半環(huán)上格林關(guān)系的開(kāi)同余

秦官偉,任苗苗,邵勇

(西北大學(xué)數(shù)學(xué)系,陜西 西安 710127)

首先給出了由半環(huán)的乘法半群上的格林關(guān)系所確定的半環(huán)開(kāi)同余的性質(zhì)和刻畫(huà).其次,由開(kāi)同余出發(fā),得到了六個(gè)不同的半環(huán)類(lèi),并證明了這六個(gè)半環(huán)類(lèi)均是半環(huán)簇.最后,對(duì)半環(huán)簇的子簇格上的開(kāi)算子進(jìn)行了探討,得到了一些有趣的結(jié)果.

半環(huán);格林關(guān)系;開(kāi)同余;半環(huán)簇;開(kāi)算子

1 引言及預(yù)備知識(shí)

許多學(xué)者研究了半環(huán)上的格林關(guān)系[3-7].在文獻(xiàn)[3]中,作者通過(guò)格林關(guān)系的開(kāi)同余代替格林關(guān)系本身,研究了半環(huán)簇和加法冪等元半環(huán)簇格上的開(kāi)算子.特別地,建立了加法冪等元半環(huán)簇的子簇格與此格上關(guān)于兩開(kāi)(閉)算子的開(kāi)(閉)簇的格的直積之間序嵌入.本文運(yùn)用開(kāi)同余,研究了半環(huán)上乘法格林關(guān)系的開(kāi)同余,半環(huán)簇和乘法冪等元半環(huán)簇的子簇格上的開(kāi)算子,給出了若干關(guān)于格林關(guān)系的半環(huán)簇之間的最小上界和最大下界,以及乘法冪等元半環(huán)的一個(gè)次直積分解.最后,利用開(kāi)同余,構(gòu)造了半環(huán)簇的子簇格上的一類(lèi)開(kāi)算子.

2 主要內(nèi)容

致謝作者對(duì)導(dǎo)師趙憲鐘教授的指導(dǎo)表示衷心感謝！

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On congruence openings of Green′s relations on a semiring

Qin Guanwei,Ren Miaomiao,Shao Yong
(Department of Mathematics,Northwest University,Xi′an 710127,China)

In this paper we fi rstly give properties and characterizations of congruence openings of a semiring that is determined by Green’s relations of multiplicative semigroup of a semiring.Secondly,we obtain six classes of semirings by means of congruence openings,and prove that these classes of semirins are all varieties of semirings.Finally,we investigate open operators on the lattice of all subvarieties of the variety of semirings and obtain some interesting results.

semiring,Green′s relation,congruence opening,variety of semirings,open operator

O153.3

A

1008-5513(2012)05-0668-08

2011-10-19.

陜西省自然科學(xué)基金(2011JQ1017);西北大學(xué)科學(xué)研究基金(NC0925).

秦官偉(1987-),碩士生,研究方向：代數(shù)學(xué).

2010 MSC:16D10