Cogroups and co-rings in categories of associative rings / George M. Bergman, Adam O. Hausknecht.

Format:

Book

Author/Creator:

Bergman, George M., 1943- author.

Hausknecht, Adam O., author.

Series:

Mathematical surveys and monographs ; no. 45.

Mathematical surveys and monographs, 0076-5376 ; volume 45

Language:

English

Subjects (All):

Associative rings.

Categories (Mathematics).

Functor theory.

Corings (Algebra).

Physical Description:

1 online resource (400 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1996]

Language Note:

English

Summary:

This book studies representable functors among well-known varieties of algebras. All such functors from associative rings over a fixed ring R to each of the categories of abelian groups, associative rings, Lie rings, and to several others are determined. Results are also obtained on representable functors on varieties of groups, semigroups, commutative rings, and Lie algebras. The book includes a "Symbol index", which serves as a glossary of symbols used and a list of the pages where the topics so symbolized are treated, and a "Word and phrase index". The authors have strived -- and succeeded -- in creating a volume that is very user-friendly.

Contents:

""Contents""; ""Chapter I. Introduction""; ""0. General prerequisites""; ""1. Introductory sketch � what are coalgebras, and why?""; ""2. Overview of results""; ""3. Results in the literature""; ""4. Notes on this book; acknowledgements""; ""Chapter II. Review of coalgebras and representable functors""; ""5. Category-theoretic formulations of universal properties, and some other matters""; ""6. Basic definitions and results of universal algebra""; ""7. Some conventions followed throughout this work""

""8. Algebra and coalgebra objects in a category, and representable algebra-valued functors""""9. Digressions on representable functors""; ""Chapter III. Representable functors from rings to abelian groups""; ""10. k-Rings""; ""11. Representable functors and pointed categories""; ""12. Plans and preparations""; ""13. Proof of the structure theorem for co-AbSemigp[sup(e)] objects""; ""14. Some immediate consequences""; ""Chapter IV. Digressions on semigroups, etc.""; ""15. Representable functors to AbBinar[sup(e)]""

""16. Representable functors to abelian semigroups without neutral element � easy results""""17. Symmetry conditions, and cocommutativity""; ""18. Application to AbSemigp-valued functors""; ""19. Some observations and questions on rings of symmetric elements""; ""20. Representable functors from Semigp[sup(e)] to Semigp[sup(e)]""; ""21. Representable functors among varieties of groups and semigroups""; ""22. Some related varieties: binars, heaps, and Mal'cev algebras""; ""Chapter V. Representable functors from algebras over a field to rings""; ""23. Bilinear maps""

""34. Functors on connected graded rings""""35. Functors from k-algebras to semigroups: some examples""; ""36. Jacobson radicals, and a general construction""; ""37. Representable functors to semigroups: toward some conjectures""; ""38. Density of invertible elements""; ""39. An idempotentless example, and a question on subfunctors""; ""Chapter VIII. Representable functors on categories of commutative associative algebras""; ""40. Some easy examples""; ""41. Identities and equational subfunctors""; ""42. Idempotents again""; ""43. Bialgebras and Hopf algebras""

""44. The Witt vector construction""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 348-359) and indexes.

Description based on print version record.

ISBN:

1-4704-1276-4