On regular rings with stable range 2

Menal, Pere; Moncasi, Jaume

doi:10.1016/0022-4049(82)90056-1

Cited by 67 publications

(19 citation statements)

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“…Now the algebra U(E) associated with the power series algebra P ((E)) has a two-sided ideal M isomorphic with the ideal of finite rank transformations on a K-vector space of countable dimension, and U(E)/M ∼ = K((x)), the field of Laurent power series. The regular ring U(E) is isomorphic to the ring constructed by Menal and Moncasi in [23,Example 1]. Finally the regular algebra Q(E) of E has a two-sided ideal J which is simple as a ring and satisfies J = Soc(Q(E)), such that Q(E)/J ∼ = K(x), the field of rational functions.…”

Section: The Regular Algebra Of a Quivermentioning

confidence: 98%

The regular algebra of a quiver

Ara

Brustenga

2007

Journal of Algebra

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Section: The Regular Algebra Of a Quivermentioning

confidence: 98%

The regular algebra of a quiver

Ara

Brustenga

2007

Journal of Algebra

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“…These conditions are equivalent for regular rings [36 [37]. It is generally regarded that, on balance, the first four of these problems ( which are seemingly independent) are likely to have negative answers.…”

Section: Strong Separativitymentioning

confidence: 99%

Separative cancellation for projective modules over exchange rings

et al. 1998

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-A separative ring is one whose finitely generated projective modules satisfy the property A EB A � A EB B � B EB B ==} A ,...., B. This condition is shown to provide a key to a number of outstanding cancellation problems for finitely generated projective modules over exchange rings. It is shown that the class of separate exchange rings is very broad, and, notably, closed under extensions of ideals by factor rings. That is, if an exchange ring R has an ideal I with I and Rf I both separative, then R is separative. SEPARATIVE CANCELLATION FOR PROJECTIVE MODULES OVER EXCHANGE RINGSP. ARA, K.R. GOODEARL, K.C. O'MEARA AND E. PARDO ABSTRACT. A separative ring is one whose finitely generated projective modules satisfy the property A EB A ~ A EB B ~ B EB B ~ A ~ B. This condition is shown to provide a key to a number of outstanding cancellation problems for finitely generated projective modules over exchange rings. It is shown that the class of separative exchange rings is very broad, and, notably, closed under extensions of ideals by factor rings. That is, if an exchange ring R has an ideal I with I and R/ I both separative, then R is separative.

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“…Note that von Neumann regular rings A satisfying sr(A) < 1 are known as unit regular rings, see [7,8,9,11,12,15]. is norr alized by all permutation matrices, we can assume that (i,j) = (l,n).…”

Section: ): a Subgroup H Of Gl" A Is Normalized By Ena If And Only Ifmentioning

confidence: 99%

Normal Subgroups of the General Linear Groups Over Von Neumann Regular Rings

Vaserstein¹

1986

Proceedings of the American Mathematical Society

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On regular rings with stable range 2

Cited by 67 publications

References 4 publications

The regular algebra of a quiver

The regular algebra of a quiver

Separative cancellation for projective modules over exchange rings

Normal Subgroups of the General Linear Groups Over Von Neumann Regular Rings

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