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Acta Mathematica Hungarica, 1997
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Groenewald, N. J., Olivier, W. A.
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Groenewald, N. J., Olivier, W. A.
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Acta Mathematica Sinica, English Series, 2002
Various results about (von Neumann) regular rings and their projective modules are carried over to ideals in regular rings. These include relations among the concepts of one-sided unit-regularity, stable rank \(1\), separativity, cancellation and substitution properties. In particular, the authors define a condition they call `the comparability' for an
Chen, Huanyin, Li, Fu-an
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Various results about (von Neumann) regular rings and their projective modules are carried over to ideals in regular rings. These include relations among the concepts of one-sided unit-regularity, stable rank \(1\), separativity, cancellation and substitution properties. In particular, the authors define a condition they call `the comparability' for an
Chen, Huanyin, Li, Fu-an
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Mediterranean Journal of Mathematics, 2018
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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 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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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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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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The regularity of munn rings and semigroup rings
Acta Mathematica Sinica, 1995A ring means an associative ring, modules over rings are left ones. A ring \(R\) is said to have the strong IBN property iff every free \(R\)- module of any rank \(n\) cannot be generated by less than \(n\) elements. Let \(M_n (R)\) denote the full matrix ring of degree \(n\) over \(R\).
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