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A minimal basis of identities for a second-order matrix algebra over a field of characteristic o

✍ Scribed by V. S. Drenski

Publisher
Springer US
Year
1981
Tongue
English
Weight
473 KB
Volume
20
Category
Article
ISSN
0002-5232

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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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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