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.
free → projective → strongly flat → condition(P) → flat → weakly flat → principally weakly flat → torsion 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
1997
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.
free → projective → strongly flat → condition(P) → flat → weakly flat → principally weakly flat → torsion 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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