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A Basis for the Graded Identities of the Matrix Algebra of Order Two over a Finite Field of Characteristic p≠2

✍ Scribed by Plamen Koshlukov; Sérgio S. Azevedo

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
155 KB
Volume
8
Category
Article
ISSN
1071-5797

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✦ Synopsis

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 graded polynomial identities for each one of these two gradings. One can distinguish these two gradings by means of the graded polynomial identities they satisfy.

📜 SIMILAR VOLUMES

Basis of the Identities of the Matrix Al
Basis of the Identities of the Matrix Algebra of Order Two over a Field of Characteristic p ≠ 2
✍ Plamen Koshlukov 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 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