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Proceedings of the American Mathematical Society

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Representation of universal algebras by sheaves

Author: U. Maddana Swamy
Journal: Proc. Amer. Math. Soc. 45 (1974), 55-58
MSC: Primary 08A25
MathSciNet review: 0340154
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Abstract: It is proved that every (universal) algebra $ A$ with distributive and permutable structure lattice is isomorphic with the algebra of all global sections with compact supports of a sheaf of homomorphic images of $ A$ over a topological space. This completely generalises the corresponding result of Klaus Keimel for $ l$-rings.

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  • [3] Klaus Keimel, The representation of lattice-ordered groups and rings by sections in sheaves, Lectures on the applications of sheaves to ring theory (Tulane Univ. Ring and Operator Theory Year, 1970–1971, Vol. III), Springer, Berlin, 1971, pp. 1–98. Lecture Notes in Math., Vol. 248. MR 0422107
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Article copyright: © Copyright 1974 American Mathematical Society