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Fundamentalnaya i Prikladnaya Matematika, 2021, Volume 23, Issue 4, Pages 209–224
(Mi fpm1917)
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Basic $\mathbb{T}$-spaces in the relatively free Grassmann algebra without unity
L. M. Tsybulya Moscow State Pedagogical Institute, Moscow, Russia
Abstract:
In this paper, we consider the $\mathbb{T}$-space structure of the relatively free Grassmann algebra $\mathbb{F}^{(3)}$ without unity over an infinite field of prime and zero characteristic. Our work is focused on $\mathbb{T}$-spaces $\mathbb{W}_n$ generated by all $n$-words. A question about connections between $\mathbb{W}_r$ and $\mathbb{W}_n$ for different natural numbers $r$ and $n$ is investigated. The proved theorem on these connections allows us to construct the diagrams of inclusions that, to some extent, clarify the structure of the algebra: the basic $\mathbb{T}$-spaces produce infinite strictly descending chains of inclusions in the algebra $\mathbb{F}^{(3)}$.
Citation:
L. M. Tsybulya, “Basic $\mathbb{T}$-spaces in the relatively free Grassmann algebra without unity”, Fundam. Prikl. Mat., 23:4 (2021), 209–224; J. Math. Sci., 269:4 (2023), 591–601
Linking options:
https://www.mathnet.ru/eng/fpm1917 https://www.mathnet.ru/eng/fpm/v23/i4/p209
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Abstract page: | 101 | Full-text PDF : | 38 | References: | 19 |
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