Remarks on representations of universal algebras by sheaves of quotient algebras

Michael Johnson, Shu-Hao Sun

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

Abstract

Nontrivial sheaf representation theorems are known for the class of algebras whose congruence lattices are distributive and the class whose congruence lattices are normal unital quantales, which include Keimel's representations of F-rings and Cornish's representations of normal lattices. Unfortunately such results do not include the sheaf representation theorems for rings with identity. In this paper, a sheaf representation for a class of universal algebras with congruence lattice containing a particular type of subframe is presented. As a consequence a representation of non commutative rings is given. This solves a problem posed by A. Wolf [in Recent advances in the representation theory of rings and C-algebras by continuous sections (New Orleans, LA, 1973), 87–93, Mem. Amer. Math. Soc., 148, Amer. Math. Soc., Providence, RI, 1974; MR0369223], but it does not yield Grothendieck representations, nor some of the representations of J. Lambek [Canad. Math. Bull. 14 (1971), 359–368; MR0313324].
Original languageEnglish
Title of host publicationCategory Theory 1991
Subtitle of host publicationProceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada
EditorsR. A. G. Seely
PublisherCanadian Mathematical Society
Pages299-307
Number of pages9
ISBN (Print)9780821860182
Publication statusPublished - 1992

Publication series

NameCanadian Mathematical Society
Volume13
ISSN (Print)0731-1036

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