秦官偉,任苗苗,邵勇

(西北大學數(shù)學系,陜西 西安 710127)

關于半環(huán)上格林關系的開同余

秦官偉,任苗苗,邵勇

(西北大學數(shù)學系,陜西 西安 710127)

首先給出了由半環(huán)的乘法半群上的格林關系所確定的半環(huán)開同余的性質和刻畫.其次,由開同余出發(fā),得到了六個不同的半環(huán)類,并證明了這六個半環(huán)類均是半環(huán)簇.最后,對半環(huán)簇的子簇格上的開算子進行了探討,得到了一些有趣的結果.

半環(huán);格林關系;開同余;半環(huán)簇;開算子

1 引言及預備知識

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

2 主要內(nèi)容

致謝作者對導師趙憲鐘教授的指導表示衷心感謝！

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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.

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

秦官偉(1987-),碩士生,研究方向：代數(shù)學.

2010 MSC:16D10