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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 12, Issue 3, Pages 303–311 (Mi mz9883)

Subalgebras of free products of algebras of the variety $\mathfrak{A}_{m,n}$

V. N. Matus

Armavirsk State Pedagogical Institute

Abstract: The variety $\mathfrak{A}_{m,n}$ is defined by the system of $n$-ary operations $\omega_1,…,\omega_m$, the system of $m$-ary operations $\varphi_1,…,\varphi_n$, $1\leqslant m\leqslant n$, and the system of identities
\begin{aligned} x_1…x_n\omega_1…x_1…x_n\omega_m\varphi_i &=x_i \qquad (i=1,…,n), x_1…x_m\varphi_1…x_1…x_m\varphi_n\omega_j &=x_j \qquad (j=1,…,m). \end{aligned}
It is proved in this paper that the subalgebra $U$ of the free product $\prod_{i\in I}^*A_i$ of the algebras $A_i$ ($i\in I$) can be expanded as the free product of nonempty intersections $U\cap A_i$ ($i\in I$) and a free algebra.

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English version:
Mathematical Notes, 1972, 12:3, 614–618

Bibliographic databases:

UDC: 512.4

Citation: V. N. Matus, “Subalgebras of free products of algebras of the variety $\mathfrak{A}_{m,n}$”, Mat. Zametki, 12:3 (1972), 303–311; Math. Notes, 12:3 (1972), 614–618

Citation in format AMSBIB
\Bibitem{Mat72} \by V.~N.~Matus \paper Subalgebras of free products of algebras of the variety $\mathfrak{A}_{m,n}$ \jour Mat. Zametki \yr 1972 \vol 12 \issue 3 \pages 303--311 \mathnet{http://mi.mathnet.ru/mz9883} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=319863} \zmath{https://zbmath.org/?q=an:0259.08003} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 3 \pages 614--618 \crossref{https://doi.org/10.1007/BF01093997}