一種廣義富足半群

高振林, 田 麗

(上海理工大學(xué)理學(xué)院,上海 200093)

一種廣義富足半群

高振林, 田 麗

(上海理工大學(xué)理學(xué)院,上海 200093)

在半群S上引進(jìn)新的Green*-關(guān)系?和R,它們雖不同于Green*-關(guān)系?*和R*,但與之有聯(lián)系,且有?*??,R*?R.引進(jìn)另一種廣義富足(或充足)半群即G-富足(或充足)半群,在G-富足半群上,引進(jìn)G-充足斷面.給出了有G-充足斷面的G-富足半群的性質(zhì)和結(jié)構(gòu).

G-富足半群;G-充足斷面;G- Green*-關(guān)系

1 預(yù)備知識(shí)

在半群S上,對(duì)a,b?S,Green*-關(guān)系R*和?*定義見(jiàn)文獻(xiàn)[1].

2 S0和I(或Λ)之間的關(guān)系

3 主要結(jié)構(gòu)定理

[1] EI-Qallali A.On the construction of a class of abundant semigroup[J].Acta Math Hung,1990,56(1/2): 77-91.

[2] HALL T E.Some properties of local subsemigroups inherited by larger subsemigroups[J].Semigroup Forum,1982,25:35-49.

[3] EI-Qallali A.Abundant semigroup with a multiplicatice type A transversal[J].Semigroup Forum,1993,47: 327-340.

[4] FOUNTAIN J B.Adequate semigroup[J].Proc Edinburgh Math Soc,1997,22:113-125.

[5] EI-Qallali A,FOUNTAIN J B.Quasi-adequate semigroups [J].Proc Roy Soc Edinburgh,1981,91A:79-99.

[6] SAITO J.Construction of regular semigroups with inverse transver-sals[J].Proc Edinburgh Math Soc, 1989,32:41-51.

[7] GAO Z L.Naturally ordered abundant semigroups with adequate transversals[J].PU M A,2003,14(1/2): 35-50.

[8] GAO Z L.On weakly commutative abundant posemigroups[J].Acta Mathematica Science(Chinese), 2001,44(4): 693-700.

On generalized abundant semigroups

GAOZhen-lin, TIANLi
(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

New Green's*-relations?G*and RG*were introduced on a semigroup S.Though they are different from the old Green's*-relations?*and R*,yet are related to each other by Green's relation on some over semigroups and it holds that?*??G*and R*?RG*.Another class of semigroups,theG- abundant(or adequate)semigroups and theirG- adequate transversals were defined and the properties and structures ofG- abundant semigroups with someG- adequate transversals were discussed.

G- abundant semigroup;G- adequate transversal;G- Green*-relation

O 152.7

A

1007-6735(2011)02-0198-07

2010-06-03

高振林(1949—),男,教授.研究方向:(序)半群理論.E-mail:zlgao@sina.com