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Nilpotent shifts on manifolds

Authors:	I I Mel'nik

Institution:	(1) Saratova State University, USSR

Abstract:	On the lattice of manifolds of all algebras L we study the operator of nilpotent closure $J:\alpha \to \alpha ^ + \mathfrak{N}$ , where $\mathfrak{N}$ is a nilpotent manifold of -algebras. With a given system of identities defining, we construct a system ^*, giving the manifold $\alpha ^ + \mathfrak{N}$ It is proved that if does not contain $\mathfrak{N}$ , then the lattice of submanifolds of $\alpha ^ + \mathfrak{N}$ is the double of the lattice of submanifolds of. We describe the free and subdirect indecomposable manifolds of algebras $\alpha ^ + \mathfrak{N}$ . Let $B \varepsilon \alpha ^ + \mathfrak{N}$ and A be adense retract of B. We denote by (B) the lattice of congruences on B. The theorem is proved: (B) is a complemented lattice if and only if (A) is a complemented lattice.Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 703–712, November, 1973.

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