منابع مشابه
Morita equivalence based on Morita context for arbitrary semigroups
In this paper, we study the Morita context for arbitrary semigroups. We prove that, for two semigroups S and T, if there exists a Morita context (S, T, P,Q, τ, μ) (not necessary unital) such that the maps τ and μ are surjective, the categories US-FAct and UT -FAct are equivalent. Using this result, we generalize Theorem 2 in [2] to arbitrary semigroups. Finally, we give a characterization of Mo...
متن کاملMorita Equivalence of Semigroups with Local Units
We prove that two semigroups with local units are Morita equivalent if and only if they have a joint enlargement. This approach to Morita theory provides a natural framework for understanding McAlister’s theory of the local structure of regular semigroups. In particular, we prove that a semigroup with local units is Morita equivalent to an inverse semigroup precisely when it is a regular locall...
متن کاملStrong Morita Equivalence of Inverse Semigroups
We introduce strong Morita equivalence for inverse semigroups. This notion encompasses Mark Lawson’s concept of enlargement. Strongly Morita equivalent inverse semigroups have Morita equivalent universal groupoids in the sense of Paterson and hence strongly Morita equivalent universal and reduced C∗-algebras. As a consequence we obtain a new proof of a result of Khoshkam and Skandalis showing t...
متن کاملStrong Morita equivalence for semigroups with local units
Morita equivalence is a widely used tool for rings with identity. (Two rings are said to be Morita equivalent if the categories of unitary modules over them are equivalent.) For monoids, this notion is not really useful: in most cases it reduces to isomorphism. As the theory of Morita equivalence could be developed for the more general case of rings with local units, and then for idempotent rin...
متن کاملOn Morita equivalence of partially ordered semigroups with local units
We show that for two partially ordered semigroups S and T with common local units, there exists a unitary Morita context with surjective maps if and only if the categories of closed right Sand T posets are equivalent.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Semigroup Forum
سال: 2015
ISSN: 0037-1912,1432-2137
DOI: 10.1007/s00233-015-9723-3