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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 $\omega_1,\dots,\omega_m$,
the system of $m$-ary operations $\varphi_1,\dots,\varphi_n$, $1\leqslant m\leqslant n$, and the system of identities
$$
\begin{aligned}
x_1\dots x_n\omega_1\dots x_1\dots x_n\omega_m\varphi_i &=x_i \qquad (i=1,\dots,n),\\
x_1\dots x_m\varphi_1\dots x_1\dots x_m\varphi_n\omega_j &=x_j \qquad (j=1,\dots,m).\\
\end{aligned}
$$
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.
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
Linking options:
https://www.mathnet.ru/eng/mzm9883 https://www.mathnet.ru/eng/mzm/v12/i3/p303
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