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A basis for the identities of the algebra of second-order matrices over a finite field

✍ Scribed by Yu. N. Mal'tsev; E. N. Kuz'min

Publisher
Springer US
Year
1978
Tongue
English
Weight
272 KB
Volume
17
Category
Article
ISSN
0002-5232

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πŸ“œ SIMILAR VOLUMES

A Basis for the Graded Identities of the
A Basis for the Graded Identities of the Matrix Algebra of Order Two over a Finite Field of Characteristic p≠2
✍ Plamen Koshlukov; SΓ©rgio S. Azevedo πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 155 KB

Let K be a finite field of characteristic p > 2, and let M 2 ðKÞ be the matrix algebra of order two over K. We describe up to a graded isomorphism the 2-gradings of M 2 ðKÞ. It turns out that there are only two nonisomorphic nontrivial such gradings. Furthermore, we exhibit finite bases of the grade

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✍ Plamen Koshlukov πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 171 KB

In this paper we prove that the polynomial identities of the matrix algebra of order 2 over an infinite field of characteristic p / 2 admit a finite basis. We exhibit a finite basis consisting of four identities, and in ''almost'' all cases for p we describe a minimal basis consisting of two identit