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2007•Algebra ColloquiumRequires access

Characterizations of Morita-like Equivalences for Right XST-Rings

Baiyu Ouyang, Liren Zhou, Wenting Tong

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Abstract

The notion of xst-rings was introduced by García and Marín in 1999. In this paper, we characterize Morita-like equivalences for right xst-rings, obtain the universal theory of Morita equivalences, and prove that two right xst-rings R and T are Morita-like equivalent if and only if there is a Morita context between R and T. We also prove that Morita-like equivalences can be realized by the covariant functors Hom and ⊗ for these rings.

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What this paper is about

The notion of xst-rings was introduced by García and Marín in 1999. In this paper, we characterize Morita-like equivalences for right xst-rings, obtain the universal theory of Morita equivalences, and prove that two right xst-rings R and T are Morita-like equivalent if and only if there is a Morita context between R and T. We also prove that Morita-like equivalences can be realized by the covariant functors Hom and ⊗ for these rings.

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Available abstract

The notion of xst-rings was introduced by García and Marín in 1999. In this paper, we characterize Morita-like equivalences for right xst-rings, obtain the universal theory of Morita equivalences, and prove that two right xst-rings R and T are Morita-like equivalent if and only if there is a Morita context between R and T. We also prove that Morita-like equivalences can be realized by the covariant functors Hom and ⊗ for these rings.

Key concepts: Morita therapy, Mathematics, Functor, Morita equivalence, Pure mathematics, Context (archaeology), Biology, Paleontology

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