On subalgebra lattices of universal algebras
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- by A. A. Iskander PDF
- Proc. Amer. Math. Soc. 32 (1972), 32-36 Request permission
Abstract:
If $Ad$ is a universal algebra, $S(A)$ is the lattice of all subalgebras of $A$. If $B \subseteq A \times A$, $B^\ast$ is $\{ (x,y) : (y,x) \in B \}$. Theorem. Let $L_1$, $L_2$, $L_3$ be algebraic lattices such that $|L_1|$, $|L_2| > 1$. Let $\alpha _i$ be an involutive automorphism of $L_i$, $i = 1$, $2$. Then there are two universal algebras $A_1$, $A_2$ of the same similarity type, having the properties: (a) there are lattice isomorphisms $\beta _i$ of $L_i$ onto $S(A_i \times A_i)$, $i = 1$, $2$, and ${\beta _3}$ of ${L_3}$ onto $S(A_1 \times A_2)$; (b) $(l \alpha _i) \beta _i = (l \beta _i)^\ast$, $l \in L_i$, $i = 1$, $2$.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 32-36
- MSC: Primary 08A25
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292733-8
- MathSciNet review: 0292733