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Morita equivalence of many-sorted algebraic theories

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
297
Issue
2
Identifiers
DOI: 10.1016/j.jalgebra.2006.01.014
Disciplines
  • Mathematics

Abstract

Abstract Algebraic theories are called Morita equivalent provided that the corresponding varieties of algebras are equivalent. Generalizing Dukarm's result from one-sorted theories to many-sorted ones, we prove that all theories Morita equivalent to an S-sorted theory T are obtained as idempotent modifications of T . This is analogous to the classical result of Morita that all rings Morita equivalent to a ring R are obtained as idempotent modifications of matrix rings of R.

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