仅含有限个极小子环的环的特性

SOME PROPERTIES OF RING WITH A FINITE NUMBER OF MINIMAL SUBRINGS

结合环R 仅含n个(n<0) 极小子环,且R 的每一真子环必含有极小子环,则R 称为M-环;若M-环R 中仪含一个极小子环,则R 称为M_1-环.本文目的是给出M-环(M_1-环)结构,从而基本上解决F.A.Szasz 提出的问题80:“怎样的环有唯一的极小子环”.

An associative ring R is called an M-ring,if every propersubring of R with finite(at least one)minimal subrings has a minimalsubring.An M-ring R is called an M_1-ring,if R has a unique minimalsubring.In this paper,some properties of an M-ring are discussed.Astructure theorem of an M_1-ring is given and problem 80 presented by Szasz:“which rings have a unique minimal subring”is solved.