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Congruence lattices of ideals in categories and (partial) semigroups /

"This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain normal subgroup lattices o...

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Bibliographic Details
Main Authors: East, James (Professor of mathematics) (Author)
Group Author: Ruškuc, Nik
Published: AMS, American Mathematical Society,
Publisher Address: Providence, RI :
Publication Dates: 2023.
Literature type: Book
Language: English
Series: Memoirs of the American Mathematical Society, volume 284, number 1408 (fourth of 6 numbers)
Subjects:
Congruences (Geometry)
Categories (Mathematics)
Semigroups.
Group theory.
Rings (Algebra)
Summary: "This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions; Brauer, Temperley-Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid categories"--
Carrier Form: vii, 129 pages : illustrations (some color) ; 26 cm.
Bibliography: Includes bibliographical references (pages 125-129).
ISBN: 9781470462697
1470462699
Index Number: QA608
CLC: O154.1
O153.1
Call Number: O153.1/E133
Contents: Categories and partial semigroups -- Ideal extensions -- Chains of ideals -- Transformation categories -- Partition categories -- Brauer categories -- Temperley-Lieb and anti-Temperley-Lieb categories -- Jones and anti-Jones categories -- Categories and partial semigroups with H -congruences -- Linear and projective linear categories -- Partial braid categories.

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