Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Stephen D. Comer, Representations by algebras of sections over Boolean spaces, Pacific J. Math. 38 (1971), 29–38. MR 0304277
  • [2] George Grätzer, Universal algebra, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1968. MR 0248066
  • [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
  • [4] 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
  • [5] A. F. Pixley, Clusters of algebras: Identities and structure lattices, Doctoral Dissertation, University of California, Berkeley, Calif., 1961.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 08A25

Retrieve articles in all journals with MSC: 08A25

Additional Information

Article copyright: © Copyright 1974 American Mathematical Society