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Geometric Algebra Over Local Rings
Bernard R. McDonald
- 01 Jan 1976
88
About: The article was published on 01 Jan 1976. and is currently open access. The article focuses on the topics: Universal geometric algebra & Filtered algebra.
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Citations
Factorization of transformations over a local ring
TL;DR: In this article, the determinant of each simple factor but one can be chosen to be any given unit in R, and the smallest number of factors needed is not greater than r + 1, where r is the codimension of the vector space associated with the module of vectors fixed under π.
14
Inducing lattice maps by semilinear isomorphisms
TL;DR: In this article, the fundamental theorem of projective geometry was generalized to larger classes of rings and the authors proved that all modules are left modules and all module homomorphisms act on the right.
13
Erdős–Ko–Rado theorem, Grassmann graphs and ps-Kneser graphs for vector spaces over a residue class ring
TL;DR: The Erdős–Ko–Rado theorem for Z p s n is obtained and some bounds of the independence number of G d are shown.
13
Similarity of matrices over Artinian principal ideal rings
TL;DR: In this paper, the theory of similarity of matrices over a commutative Artinian principal ideal ring R is discussed and it is shown that for the class matrices A such that R [ A ] is R -free a "rational" canonical form is available.
12
Products of quasireflections and transvections over local rings
Erich W. Ellers,Rolfdieter Frank +1 more
TL;DR: In this article, the minimal number of factors needed in any factorization of π of a free R-module of rank n is shown to be a product of quasireflections or transvections.
11
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