Limit T-spaces |
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Authors: | E A Kireeva |
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Institution: | (1) Moscow Pedagogical State University, Moscow, Russia |
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Abstract: | Let F be a field of prime characteristic p and let V
p be the variety of associative algebras over F without unity defined by the identities x, y], z] = 0 and x
4 = 0 if p = 2 and by the identities x, y], z] = 0 and x
p = 0 if p > 2 (here x, y] = xy − yx). Let A/V
p be the free algebra of countable rank of the variety V
p and let S be the T-space in A/V
p generated by x
12
x
22 ⋯ x
k2 + V
2, where k ∈ ℕ if p = 2, and by {ie4170-01}, where k ∈ ℕ and α
1, …, α
2k
∈ {0, p − 1} if p > 2. As is known, S is not finitely generated as a T-space. In the present paper, we prove that S is a limit T-space, i.e., a maximal nonfinitely generated T-space. As a corollary, we have constructed a limit T-space in
the free associative F-algebra without unity of countable rank.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 1, pp. 135–159, 2007. |
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Keywords: | |
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