n-GB环和n-NGB环
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摘要
给出n-GB环和n-NGB环的概念,得到如下结论:1)当且仅当V_2(R)是2-GB环,或GT_3(R)及M_2~((1,4))(R)为2-NGB环时,R为Boolean环;2)2-NGB环为quasi-normal环;3)设I_1,I_2为R的理想,I_1∩I_2=0,则R为n-GB环当且仅当R/I_1,R/I_2为n-GB环.
In this paper,the definitions of n-GB rings and n-NGB rings are given.The main results are as follows.1)Ris a Boolean ring if and only if V_2(R)is a 2-GB ring,GT_3(R)or M_2~((1,4))(R)is a2-NGB ring;2)2-NGB rings are quasi-normal;3)Let I_1,I_2 be ideals of R,and I_1∩I_2=0.Then R is a n-GB ring if and only if R/I_1 and R/I_2 are n-GB rings.
In this paper,the definitions of n-GB rings and n-NGB rings are given.The main results are as follows.1)Ris a Boolean ring if and only if V_2(R)is a 2-GB ring,GT_3(R)or M_2~((1,4))(R)is a2-NGB ring;2)2-NGB rings are quasi-normal;3)Let I_1,I_2 be ideals of R,and I_1∩I_2=0.Then R is a n-GB ring if and only if R/I_1 and R/I_2 are n-GB rings.
引文
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[10]ZHOU Ying,WEI Junchao.Generalized weakly central reduced rings[J].Turk Math J,2015,39(5):604-617.
[11]屈寅春,周颖,魏俊潮.Abel环的一些刻画[J].扬州大学学报(自然科学版),2012,15(4):5-7.
[2]BOUDET A,JOUANNAUD J P,SCHMIDT-SCHAUSS M.Unification in Boolean rings and Abelian groups[J].J Symb Comput,1989,8(5):449-477.
[3]LAGRANGE J D.Complemented zero-divisor graphs and Boolean rings[J].J Algebra,2007,315(2):600-611.
[4]ABU-KHUZAM H,YAQUB A.Boolean-like rings and related rings[J].Int J Algebra,2011,5(6):275-284.
[5]王秀兰.半Boolean群环[J].山东大学学报(理学版),2012,47(10):33-38.
[6]HSIANG J,HUANG G S.Some fundamental properties of Boolean ring normal forms[J].DIMACS Ser Discrete Math Theoret Comput Sci,1997,35(4):587-602.
[7]秦蕊.Boolean-like环及其推广的研究[D].杭州:杭州师范大学,2014.
[8]ALEXANDER A.Boolean rings of sets with finite subcovering property[J].Math Nachr,1970,47(1):77-78.
[9]WEI Junchao.LI Libin.Quasi-normal rings[J].Comm Algebra,2010,38(5):1855-1868.
[10]ZHOU Ying,WEI Junchao.Generalized weakly central reduced rings[J].Turk Math J,2015,39(5):604-617.
[11]屈寅春,周颖,魏俊潮.Abel环的一些刻画[J].扬州大学学报(自然科学版),2012,15(4):5-7.