Complete reducibility in exterior algebras over free modules
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This article is published in Journal of Algebra.The article was published on 1968-11-01 and is currently open access. It has received 23 citations till now. The article focuses on the topics: Lie coalgebra & Clifford algebra.read more
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Algebraic vector bundles over $$\mathbb{A}^3 $$ are trivial
M. Pavaman Murthy,Jacob Towber +1 more
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Composition of oriented binary quadratic form-classes over commutative rings
TL;DR: In this article, a binary quadratic form a x e + bxy + cy 2 with integral coefficients is called primitive if a, b, c have g.c.d. 1, and is called "properly equivalent" to any form obtained from it by a linear transformation with integral coefficient and determinant + 1.
Book ChapterDOI
Factorizations of Elements in Noncommutative Rings: A Survey
TL;DR: A survey of non-zero-divisor factorizations in non-commutative rings can be found in this paper, with a focus on the commutative theory of nonunique factorizations.
Journal ArticleDOI
Similarity and commutators of matrices over principal ideal rings
TL;DR: In this article, it was shown that if a matrix is a principal ideal ring and is a matrix with trace zero, then it is a commutator, that is, for some.
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Matrix factorizations, exterior powers, and complete intersections
TL;DR: In this paper, the Morita correspondence between submodules of R and left ideals in R has been studied in the context of matrix factorization, and it has been shown that the existence of such a factor is equivalent to weak norm-induced factorization.
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Ideals defined by matrices and a certain complex associated with them
TL;DR: In this paper, a generalization of the standard Koszul complex is defined for the case of a matrix with only a single row and it is shown that such an ideal has finite projective dimension whenever its grade reaches a certain greatest value (depending on the dimensions of the matrix).
Sur les modules projectifs
TL;DR: In this paper, Séminaire Dubreil implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
MonographDOI
Rings and Ideals
TL;DR: The Carus Mathematical Monographs as mentioned in this paper is a collection of early abstract algebra books focusing on the theory of rings, with some emphasis on the role of ideals in the theory.