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Search: MSC category 16S10 ( Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) )

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1. CMB Online first

Ara, Pere; O'Meara, Kevin C.
 The Nilpotent Regular Element Problem We use George Bergman's recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element $x$ need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent element $x$ are regular. Keywords:nilpotent element, von Neumann regular element, unit-regular, Bergman's normal formCategories:16E50, 16U99, 16S10, 16S15

2. CMB 2000 (vol 43 pp. 3)

Adin, Ron; Blanc, David
 Resolutions of Associative and Lie Algebras Certain canonical resolutions are described for free associative and free Lie algebras in the category of non-associative algebras. These resolutions derive in both cases from geometric objects, which in turn reflect the combinatorics of suitable collections of leaf-labeled trees. Keywords:resolutions, homology, Lie algebras, associative algebras, non-associative algebras, Jacobi identity, leaf-labeled trees, associahedronCategories:18G10, 05C05, 16S10, 17B01, 17A50, 18G50
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