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Trace- and pseudo-products: restriction-like semigroups with a band of projections

journal contribution
posted on 2023-05-21, 05:37 authored by Desmond FitzGeraldDesmond FitzGerald, Kinyon, MK
We ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem and its generalisation to ample semigroups. Unlike some other variants of ESN, it is self-dual (two-sided), and the condition of commuting projections is relaxed. The condition that projections form a band (are closed under multiplication) is shown to be a very natural one. One-sided reducts are considered, and compared to (generalised) D-semigroups. Finally the special case when the category is a groupoid is examined.

History

Publication title

Semigroup Forum

Volume

103

Pagination

848-866

ISSN

0037-1912

Department/School

School of Natural Sciences

Publisher

Springer-Verlag

Place of publication

175 Fifth Ave, New York, USA, Ny, 10010

Rights statement

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021

Repository Status

  • Restricted

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Expanding knowledge in the mathematical sciences

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