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010 a| 2023014514;

020 a| 9781470462697q| (paperback);

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100 1 a| East, Jamesc| (Professor of mathematics)?| UNAUTHORIZED;

245 10 a| Congruence lattices of ideals in categories and (partial) semigroupsh| [electronic resource] /c| James East, Nik Ruškuc.;

260 a| Providence, RI :b| AMS, American Mathematical Society,c| 2023.;

300 a| vii, 129 pages :b| illustrations ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 284, number 1408;

504 a| Includes bibliographical references (pages 125-129).;

505 0 a| 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.;

506 a| Available only to authorized users.;

520 a| "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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Congruences (Geometry)=| ^A278043;

650 0 a| Categories (Mathematics)=| ^A23638;

650 0 a| Semigroups.=| ^A52496;

650 7 a| Group theory and generalizations -- Semigroups -- Semigroups of transformations, etc..2| msc;

650 7 a| General algebraic systems -- Algebraic structures -- Subalgebras, congruence relations.2| msc;

650 7 a| Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Linear transformations, semilinear transformations.2| msc;

650 7 a| Category theory; homological algebra -- Special categories -- Groupoids, semigroupoids, semigroups, groups (viewed as categories).2| msc;

650 7 a| Group theory and generalizations -- Semigroups -- General structure theory.2| msc;

650 7 a| Group theory and generalizations -- Semigroups -- Connections of semigroups with homological algebra and category theory.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Ruškuc, Nik.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30539177;

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Congruence lattices of ideals in categories and (partial) semigroups / James East, Nik Ruškuc.

Author/creator	East, James
Other author	Ruškuc, Nik.
Format	Electronic
Publication Info	Providence, RI : AMS, American Mathematical Society, 2023.
Description	vii, 129 pages : illustrations ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Congruences (Geometry) Categories (Mathematics) Semigroups.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 284, number 1408
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.
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 125-129).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023014514
ISBN	9781470462697 (paperback)
ISBN	(pdf)

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Congruence lattices of ideals in categories and (partial) semigroups / James East, Nik Ruškuc.

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