共查询到17条相似文献,搜索用时 46 毫秒
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A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. In this paper, we study the regularity of right SF-rings and prove that if R is a right SF-ring whose all maximal (essential) right ideals are GW-ideals, then R is regular. 相似文献
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以正则环为桥梁,研究了morphic-环与SF-环之间的关系.主要工作如下:(i)研究了SF-环成为morphic-环的若干条件;(ii)讨论了在一定条件下SF-环与morphic-环的等价性;(iii)给出了利用morphic-环对半单环在约化条件下的一个刻划. 相似文献
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关于GP-V-环与强正则环的刻划 总被引:2,自引:0,他引:2
The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown. 相似文献
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研究了每一个极大左理想是弱右理想的环的性质.得到了SF-环和强正则环的一些新的刻画,推广了一些已知的结论. 相似文献
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研究了每一个极大左理想是弱右理想的环的性质.得到了左SF-环和强正则环的一些新的刻画,推广了一些已知的结论. 相似文献
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Haiyan Zhou 《代数通讯》2013,41(12):3842-3850
A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. In this article, we study the regularity of left SF-rings and we prove the following: 1) if R is a left SF-ring whose all complement left (right) ideals are W-ideals, then R is strongly regular; 2) if R is a left SF-ring whose all maximal essential right ideals are GW-ideals, then R is regular. 相似文献
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von Neumann Regular Rings and Right SF-rings 总被引:2,自引:0,他引:2
A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. In this paper, we study the regularity of right SF-rings and prove that if R is a right SF-ring whose all maximal (essential) right ideals are GW-ideals, then R is regular. 相似文献
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On Real Closed Regular Rings 总被引:1,自引:0,他引:1
Zhizhong Dai 《Algebra Colloquium》2003,10(1):91-94
The aim of this paper is to investigate some properties of real closed regular rings, in particular, the role played by real place in a real closed regular ring.2000 Mathematics Subject Classification: 13J25This work was supported by NSF of Jiangxi Province, China. 相似文献
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本文分别讨论了关于结合环和半群的二个定理,并且由结合环的这二个定理推出了如下准则:结合环R是Abel正则的,当且仅当R的每个拟理想是正则环. 相似文献
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In this paper we introduce a construction called the skew generalized power series ring R[[S, ω]] with coefficients in a ring R and exponents in a strictly ordered monoid S which extends Ribenboim's construction of generalized power series rings. In the case when S is totally ordered or commutative aperiodic, and ω(s) is constant on idempotents for some s ∈ S?{1}, we give sufficient and necessary conditions on R and S such that the ring R[[S, ω]] is von Neumann regular, and we show that the von Neumann regularity of the ring R[[S, ω]] is equivalent to its semisimplicity. We also give a characterization of the strong regularity of the ring R[[S, ω]]. 相似文献
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关于环的极大本质右理想 总被引:7,自引:0,他引:7
设R为环,我们考虑下面两个条件。(*)R的每个极大本质右理想是GP-内射右R-模或右零化子.(*)R的每个极大本质右理想是YJ-内射右R-模.本文旨在研究满足条件(*)或(*)的环,同时我们还给出了强正则环和除环的一些新刻画. 相似文献