Morita Equivalence for Rings with Involution

Pere Ara

doi:10.1023/A:1009958527372

Morita Equivalence for Rings with Involution

Pere Ara

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

20 Citations (Scopus)

Abstract

We develop the theory of Morita equivalence for rings with involution, and we show the corresponding fundamental representation theorem. In order to allow applications to operator algebras, we work within the class of idempotent nondegenerate rings. We also prove that two commutative rings with involution are Morita *-equivalent if and only if they are *-isomorphic.

Original language	English
Pages (from-to)	227-247
Journal	Algebras and Representation Theory
Volume	2
Issue number	3
DOIs	https://doi.org/10.1023/A:1009958527372
Publication status	Published - 1 Sep 1999

Keywords

Idempotent rings
Inner product
Morita equivalence
Rings with involution

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abstract = "We develop the theory of Morita equivalence for rings with involution, and we show the corresponding fundamental representation theorem. In order to allow applications to operator algebras, we work within the class of idempotent nondegenerate rings. We also prove that two commutative rings with involution are Morita *-equivalent if and only if they are *-isomorphic.",

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N2 - We develop the theory of Morita equivalence for rings with involution, and we show the corresponding fundamental representation theorem. In order to allow applications to operator algebras, we work within the class of idempotent nondegenerate rings. We also prove that two commutative rings with involution are Morita *-equivalent if and only if they are *-isomorphic.

AB - We develop the theory of Morita equivalence for rings with involution, and we show the corresponding fundamental representation theorem. In order to allow applications to operator algebras, we work within the class of idempotent nondegenerate rings. We also prove that two commutative rings with involution are Morita *-equivalent if and only if they are *-isomorphic.

KW - Idempotent rings

KW - Inner product

KW - Morita equivalence

KW - Rings with involution

U2 - 10.1023/A:1009958527372

DO - 10.1023/A:1009958527372

M3 - Article

VL - 2

SP - 227

EP - 247

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

IS - 3

ER -