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Homological classification of monoids

Homological classification of monoids
Homological classification of monoids

We deal in this thesis with what is generally referred to as homological classification of monoids by properties of their acts. We have the following hierarchy of properties arranged in strictly decreasing order of strength such that a given act may or may not possess.

freeprojectivestrongly flatcondition(P) flatweakly flatprincipally weakly flattorsion free

Many papers have appeared describing classes of monoids over which various of the above distinct properties coincide either for all acts or for all acts of a certain type.

There are monoids such that exact descriptions of their class have not yet been determined, although partial results may be known.

In this work the classification of monoids by condition (P) of (weakly) flat (cyclic) right acts, condition (E), properties of principal ideals, generators and regular acts has been considered. Also by introducing new conditions (PE), (P'E), and (P1E) we classify some monoids by these conditions.

University of Southampton
Golchin, Akbar
78a9cc5a-c534-4792-999c-8ad545a90769
Golchin, Akbar
78a9cc5a-c534-4792-999c-8ad545a90769

Golchin, Akbar (1997) Homological classification of monoids. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

We deal in this thesis with what is generally referred to as homological classification of monoids by properties of their acts. We have the following hierarchy of properties arranged in strictly decreasing order of strength such that a given act may or may not possess.

freeprojectivestrongly flatcondition(P) flatweakly flatprincipally weakly flattorsion free

Many papers have appeared describing classes of monoids over which various of the above distinct properties coincide either for all acts or for all acts of a certain type.

There are monoids such that exact descriptions of their class have not yet been determined, although partial results may be known.

In this work the classification of monoids by condition (P) of (weakly) flat (cyclic) right acts, condition (E), properties of principal ideals, generators and regular acts has been considered. Also by introducing new conditions (PE), (P'E), and (P1E) we classify some monoids by these conditions.

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Published date: 1997

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Local EPrints ID: 463246
URI: http://eprints.soton.ac.uk/id/eprint/463246
PURE UUID: 0652ba1d-357e-4057-a74e-4ea25bd11b0d

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Date deposited: 04 Jul 2022 20:48
Last modified: 16 Mar 2024 19:03

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Author: Akbar Golchin

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