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Russian Mathematics, 2011
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Semiregular, weakly regular, and π-regular rings
Journal of Mathematical Sciences, 2002This is a survey paper related to regular rings and their generalizations. It introduces many rings and modules, such as: semiregular and regular modules, semiregular and regular rings, semiprime and nonsingular rings, weakly \(\pi\)-regular and weakly regular rings, strongly \(\pi\)-regular and \(\pi\)-regular rings, rings of quotients and Pierce ...
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Mediterranean Journal of Mathematics, 2018
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Chen, Huanyin +2 more
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Siberian Mathematical Journal, 2004
Summary: We extend the well-known result by \textit{S. Burris} and \textit{H. Werner} [Trans. Am. Math. Soc. 248, 269--309 (1979; Zbl 0411.03022)] on existence of defining sequences for elementary products of models to arbitrary enrichments of Boolean algebras (we obtain a complete analog of the Feferman -- Vaught theorem). This enables us to establish
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Summary: We extend the well-known result by \textit{S. Burris} and \textit{H. Werner} [Trans. Am. Math. Soc. 248, 269--309 (1979; Zbl 0411.03022)] on existence of defining sequences for elementary products of models to arbitrary enrichments of Boolean algebras (we obtain a complete analog of the Feferman -- Vaught theorem). This enables us to establish
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Algebraically Closed Regular Rings
Canadian Journal of Mathematics, 1974In this paper all rings are commutative and have a unity. All ring homomorphisms preserve the unity. We let L denote the standard language for rings with two distinct constants, 0 and 1, playing the role of the zero and the unity respectively. A ring is regular if it satisfies the axiom (∀r) (∃r′)(rr′r = r) and it is algebraically closed if, for each ...
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Mathematika, 1956
In the following pages there will be found an account of the properties of a certain class of local rings which are here termed semi-regular local rings . As this name will suggest, these rings share many properties in common with the more familiar regular local rings, but they form a larger class and the characteristic properties are preserved under ...
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In the following pages there will be found an account of the properties of a certain class of local rings which are here termed semi-regular local rings . As this name will suggest, these rings share many properties in common with the more familiar regular local rings, but they form a larger class and the characteristic properties are preserved under ...
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Canadian Mathematical Bulletin, 1961
A subset K of a lattice is said to be directed if for any a, b∊K there is c∊K with c ≥ a, b. A complete lattice L is called upper continuous if for every directed subset (aα) and every element b.The following is a slight improvement of [4; Anmerkung 1. 11, p. 11].
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A subset K of a lattice is said to be directed if for any a, b∊K there is c∊K with c ≥ a, b. A complete lattice L is called upper continuous if for every directed subset (aα) and every element b.The following is a slight improvement of [4; Anmerkung 1. 11, p. 11].
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Regular self-injective rings andV-rings
Algebra and Logic, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Summary: In this paper we introduce the concepts of special regular clean elements and regular clean decomposition in a ring \(R\). These concepts lead us to the notion of special regular clean ring. We prove that for a special regular clean element \(a = e + r\in R\) and unit \(u\in R\) then \(au\) is a special regular clean if \(u\) is an inner ...
Gogoi, Saurav, Saikia, Helen
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Gogoi, Saurav, Saikia, Helen
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Proceedings of the American Mathematical Society, 1973
Armendariz, E. P., Fisher, Joe W.
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Armendariz, E. P., Fisher, Joe W.
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