Abstract:
Let $M_{1,1}$ be the matrix superalgebra over an infinite field of positive characteristic $p\ne2$. Multilinear identities of prime subvarieties in the variety $\operatorname{Var}M_{1,1}$ are described. It is shown that the set of multilinear identities of any prime subvariety in the variety $\operatorname{Var}M_{1,1}$ either coincides with the set of multilinear identities of the algebra $M_{1,1}$ or is generated by the identity $[x,y,z]=0$ or is generated by the identity $[x,y]=0$.
Keywords:prime subvariety, matrix superalgebra, multilinear identities, variety of associative algebras, Grassmann algebra, prime variety.
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