Nilpotent shifts on manifolds |
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Authors: | I. I. Mel'nik |
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Affiliation: | (1) Saratova State University, USSR |
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Abstract: | On the lattice of manifolds of all algebras L we study the operator of nilpotent closure, where is a nilpotent manifold of -algebras. With a given system of identities defining, we construct a system *, giving the manifold It is proved that if does not contain, then the lattice of submanifolds of is the double of the lattice of submanifolds of. We describe the free and subdirect indecomposable manifolds of algebras. Let 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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