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- W1993215545 abstract "Let F be a field and let F〈X〉 be the free unital associative F-algebra on the free generating set X={x1,x2,…}. A subalgebra (a vector subspace) V in F〈X〉 is called a T-subalgebra (a T-subspace) if ϕ(V)⊆V for all endomorphisms ϕ of F〈X〉. For an algebra G, its central polynomials form a T-subalgebra C(G) in F〈X〉. Over a field of characteristic p>2 there are algebras G whose algebras of all central polynomials C(G) are not finitely generated as T-subspaces in F〈X〉. However, no example of an algebra G such that C(G) is not finitely generated as a T-subalgebra is known yet. In the present paper we construct the first example of a 2-graded unital associative algebra B over a field of characteristic p>2 whose algebra C2(B) of all 2-graded central polynomials is not finitely generated as a T2-subalgebra in the free 2-graded unital associative F-algebra F〈Y,Z〉. We hope that our example will help to construct an algebra G whose algebra C(G) of (ordinary) central polynomials is not finitely generated as a T-subalgebra in F〈X〉." @default.
- W1993215545 created "2016-06-24" @default.
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- W1993215545 date "2015-03-01" @default.
- W1993215545 modified "2023-10-15" @default.
- W1993215545 title "The subalgebra of graded central polynomials of an associative algebra" @default.
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- W1993215545 doi "https://doi.org/10.1016/j.jalgebra.2014.11.022" @default.
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