{"title":"Mathematics: Algebra","description":"","products":[{"product_id":"algebra","title":"Algebra","description":"\u003cspan data-mce-fragment=\"1\"\u003eFrom rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory.\u003c\/span\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":39870734434480,"sku":"9781108958233","price":29.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781108958233.jpg?v=1622355353"},{"product_id":"pseudo-reductive-groups","title":"Pseudo-reductive Groups","description":"Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43411912818927,"sku":"9781107087231","price":109.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781107087231i.jpg?v=1664198889"},{"product_id":"homological-theory-of-representations","title":"Homological Theory of Representations","description":"Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":44264809857263,"sku":"9781108838894","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9781108838894i.jpg?v=1701090285"},{"product_id":"sale-linear-algebra","title":"SALE Linear Algebra","description":"\u003cp data-mce-fragment=\"1\"\u003e\u003cstrong data-mce-fragment=\"1\"\u003eThis book is unused and unread. It has some cosmetic imperfections such as scuffing, creasing and fading. It may be stamped 'damaged'.\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp data-mce-fragment=\"1\"\u003e\u003cstrong data-mce-fragment=\"1\"\u003e\u003cspan data-mce-fragment=\"1\"\u003eThis book cannot be discounted further.\u003c\/span\u003e\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003eAny student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.\u003c\/p\u003e\n\u003cdiv class=\"contentHidden\"\u003e\n\u003cul class=\"academicArrowList\"\u003e\n\u003cli\u003eSuitable as a course text and also ideal for self-study\u003c\/li\u003e\n\u003cli\u003eHundreds of exercises and solutions provide plenty of hands-on practice\u003c\/li\u003e\n\u003cli\u003eEasier to navigate than other lengthy texts\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/div\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":44493927743727,"sku":"9780521279482","price":27.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9780521279482i.jpg?v=1707406790"},{"product_id":"sale-how-groups","title":"SALE How Groups Grow","description":"\u003cp\u003e\u003cstrong\u003eThis book is unused and unread. It has some cosmetic imperfections such as scuffing, tearing and creasing. It is stamped 'damaged'. No further discounts. \u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003eGrowth of groups is an innovative new branch of group theory. This is the first book to introduce the subject from scratch. It begins with basic definitions and culminates in the seminal results of Gromov and Grigorchuk and more. The proof of Gromov's theorem on groups of polynomial growth is given in full, with the theory of asymptotic cones developed on the way. Grigorchuk's first and general groups are described, as well as the proof that they have intermediate growth, with explicit bounds, and their relationship to automorphisms of regular trees and finite automata. Also discussed are generating functions, groups of polynomial growth of low degrees, infinitely generated groups of local polynomial growth, the relation of intermediate growth to amenability and residual finiteness, and conjugacy class growth. This book is valuable reading for researchers, from graduate students onward, working in contemporary group theory.\u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":56607012422018,"sku":"9781107657502","price":42.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9781107657502i.jpg?v=1777737917"},{"product_id":"sale-elements-of-the-representation-theory-of-associative-algebras","title":"SALE Elements of the Representation Theory of Associative Algebras","description":"\u003cp\u003e\u003cstrong\u003eThis book is unused and unread. It has some cosmetic imperfections such as scuffing, tearing and creasing. It is stamped 'damaged'. No further discounts. \u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003eThe final part of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers and homological algebra. This volume provides an introduction to the representation theory of representation-infinite tilted algebras from the point of view of the time-wild dichotomy. Also included is a collection of selected results relating to the material discussed in all three volumes. The book is primarily addressed to a graduate student starting research in the representation theory of algebras, but will also be of interest to mathematicians in other fields. Proofs are presented in complete detail, and the text includes many illustrative examples and a large number of exercises at the end of each chapter, making the book suitable for courses, seminars, and self-study.\u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":56648684241282,"sku":"9780521708760","price":29.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9780521708760i.jpg?v=1778682721"},{"product_id":"sale-the-block-theory-of-finite-group-algebras","title":"SALE The Block Theory of Finite Group Algebras","description":"\u003cp\u003e\u003cstrong\u003eThis book is unused and unread. It has some cosmetic imperfections such as scuffing, tearing and creasing. It is stamped 'damaged'. No further discounts. \u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003eThis is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.\u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":56648838807938,"sku":"9781108441803","price":30.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9781108441803i_1.jpg?v=1778684739"}],"url":"https:\/\/www.cambridgebookshop.co.uk\/collections\/mathematics-algebra.oembed","provider":"Cambridge University Press Bookshop","version":"1.0","type":"link"}