Diophantine unsolvability for function fields over certain infinite fields of characteristic p

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; Sérgio S. Azevedo 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 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