Results 241 to 250 of about 394,267 (278)
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Canadian Mathematical Bulletin, 1973
This paper attempts to generalize a property of regular rings, namely,I2=Ifor every right (left) ideal. Rings with this property are called right (left) weakly regular. A ring which is both left and right weakly regular is called weakly regular. Kovacs in [6] proved that, for commutative rings, weak regularity and regularity are equivalent conditions ...
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This paper attempts to generalize a property of regular rings, namely,I2=Ifor every right (left) ideal. Rings with this property are called right (left) weakly regular. A ring which is both left and right weakly regular is called weakly regular. Kovacs in [6] proved that, for commutative rings, weak regularity and regularity are equivalent conditions ...
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Regular Rings are Very Regular
Canadian Mathematical Bulletin, 1982The following problem arose in a conversation with Abraham Zaks: “Suppose R is an associative ring with identity such that every finitely generated left ideal is generated by idempotents. Is R von-Neumann regular?” In the literature the “s” in “idempotents” is missing, and is replaced by “an idempotent”. The answer is, “Yes!”
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Canadian Journal of Mathematics, 1965
1.1. Throughout this note, will denote an associative ring but we shall not require to possess a unit.If A and B are subsets of , then A + B will denote the set {x + y| x ∊ A, y ∊ B}. Aτ will denote the set {u ∊ | au = 0 for all a ∊ A} .Elements a and b will be said to be orthogonal if ab = ba = 0.
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1.1. Throughout this note, will denote an associative ring but we shall not require to possess a unit.If A and B are subsets of , then A + B will denote the set {x + y| x ∊ A, y ∊ B}. Aτ will denote the set {u ∊ | au = 0 for all a ∊ A} .Elements a and b will be said to be orthogonal if ab = ba = 0.
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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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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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