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This article is cited in 13 scientific papers (total in 13 papers)
Nilpotent shifts on manifolds
I. I. Mel'nik Saratov State University
Abstract:
On the lattice of manifolds of all algebras $L$ we study the operator of nilpotent closure $J:\alpha\to\alpha+\mathfrak{R}$, where $\mathfrak{R}$ is a nilpotent manifold of $\Omega$-algebras. With a given system of identities $\Sigma$ defining $\alpha$, we construct a system $\Sigma^*$, giving the manifold $\alpha+\mathfrak{R}$. It is proved that if $\alpha$ does not contain $\mathfrak{R}$, then the lattice of submanifolds of $\alpha+\mathfrak{R}$ is the double of the lattice of submanifolds of $\alpha$. We describe the free and subdirect indecomposable manifolds of algebras $\alpha+\mathfrak{R}$. Let $B\in\alpha+\mathfrak{R}$ and $A$ be a dense retract of $B$. We denote by $\theta(B)$ the lattice of congruences on $B$. The theorem is proved: $\theta(B)$ is a complemented lattice if and only if $\theta(A)$ is a complemented lattice.
Received: 12.07.1972
Citation:
I. I. Mel'nik, “Nilpotent shifts on manifolds”, Mat. Zametki, 14:5 (1973), 703–712; Math. Notes, 14:5 (1973), 962–966
Linking options:
https://www.mathnet.ru/eng/mzm9955 https://www.mathnet.ru/eng/mzm/v14/i5/p703
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Abstract page: | 119 | Full-text PDF : | 55 | First page: | 1 |
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