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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
Received: 18.05.1971

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}


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