Representation of universal algebras by sheaves
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- by U. Maddana Swamy PDF
- Proc. Amer. Math. Soc. 45 (1974), 55-58 Request permission
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.References
- Stephen D. Comer, Representations by algebras of sections over Boolean spaces, Pacific J. Math. 38 (1971), 29–38. MR 304277
- George Grätzer, Universal algebra, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1968. MR 0248066
- 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), Lecture Notes in Math., Vol. 248, Springer, Berlin, 1971, pp. 1–98. MR 0422107
- R. S. Pierce, Modules over commutative regular rings, Memoirs of the American Mathematical Society, No. 70, American Mathematical Society, Providence, R.I., 1967. MR 0217056 A. F. Pixley, Clusters of algebras: Identities and structure lattices, Doctoral Dissertation, University of California, Berkeley, Calif., 1961.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 55-58
- MSC: Primary 08A25
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340154-3
- MathSciNet review: 0340154