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K-Theoretically Simple Von Neumann Regular Rings
Journal of Algebra, 1995 The authors investigate the differences between simplicity of a von Neumann regular ring and simplicity of its ordered Grothendieck group \(K_0\). After giving preliminaries in \S 1, they derive properties of pseudo-rank functions on ideals in a regular ring. In \S 3 they prove that if \(R\) is a stably finite, \(K_0\)-simple, non-Artinian regular ring
Ara, P. +3 more
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Self-injective von Neumann regular rings and Köthe's conjecture [PDF]
Journal of Pure and Applied Algebra, 2021 One of the many equivalent formulation of the K the's conjecture is the assertion that there exists no ring which contains two nil right ideals whose sum is not nil. We discuss several consequences of an observation that if the Koethe conjecture fails then there exists a counterexample in the form of a countable local subring of a suitable self ...
Kálnai, Peter, Žemlička, Jan
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A Generalized Primitive Element Theorem [PDF]
, 2007 We deal with the following variant of the primitive element theorem: any commutative strongly separable extension of a commutative ring can be embedded in another one having primitive element.
Bagio, Dirceu, Paques, Antonio
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On von Neumann regular rings - II.
MATHEMATICA SCANDINAVICA, 1976 As in other papers of this long series [for Part X see Collect. Math. 34, 81-94 (1983; Zbl 0544.16006), Part XIII see Ann. Univ. Ferrara, Nuova Ser., Sez. VII 31, 49-61 (1985; Zbl 0588.16006)], the author considers generalizations of concepts such as regularity and injectivity.
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Vertex rings and their Pierce bundles
, 2017 In part I we introduce vertex rings, which bear the same relation to vertex algebras (or VOAs) as commutative, associative rings do to commutative, associative algebras over the complex numbers.
Mason, Geoffrey
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From regular modules to von Neumann regular rings via coordinatization [PDF]
Romanian Journal of Mathematics and Computer Science, 2014 In this paper we establish a very close link (in terms of von Neu- mann's coordinatization) between regular modules introduced by Zel- manowitz, on one hand, and von Neumann regular rings, on the other hand: we prove that the lattice L^{fg}(M) of all ...
Leonard Daus, Mohamed A. Salim
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Cyclically presented modules, projective covers and factorizations
, 2013 We investigate projective covers of cyclically presented modules, characterizing the rings over which every cyclically presented module has a projective cover as the rings $R$ that are Von Neumann regular modulo their Jacobson radical $J(R)$ and in which
Facchini, Alberto +2 more
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Gorenstein Von Neumann regular rings
, 2009 In this paper, we study the rings with zero Gorenstein weak dimensions, which we call them Gorenstein Von Neumann regular rings.
Mahdou, Najib +2 more
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Polynomial Rings Over a Commutative von Neumann Regular Ring [PDF]
Proceedings of the American Mathematical Society, 1975 It is shown that the annihilator of each finitely generated ideal of R [ { X λ } λ ∈ Λ ] R[{\{ {X_\lambda }\} _{\lambda \in \Lambda ...
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Two New Types of Rings Constructed from Quasiprime Ideals
International Journal of Mathematics and Mathematical Sciences, 2011 Keigher showed that quasi-prime ideals in differential commutative rings are analogues of prime ideals in commutative rings. In that direction, he introduced and studied new types of differential rings using quasi-prime ideals of a differential ring.
Manal Ghanem, Hassan Al-Ezeh
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