{"product_id":"9789814571449","title":"Lecture Notes On Algebraic Structure Of Lattice-ordered Rings","description":"\u003cp\u003e\u003ci\u003eAlgebraic Structure of Lattice-Ordered Rings\u003c\/i\u003e presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field.\u003c\/p\u003e\u003cp\u003eThis book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book.\u003c\/p\u003e\u003cp\u003eThe book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eIntroduction to Ordered Algebraic Systems:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eLattices\u003c\/li\u003e\n\u003cli\u003eLattice-Ordered Groups and Vector Lattices\u003c\/li\u003e\n\u003cli\u003eLattice-Ordered Rings and Algebras\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eLattice-Ordered Algebras with a d-Basis:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eExamples and Basic Properties\u003c\/li\u003e\n\u003cli\u003eStructure Theorems\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003ePositive Derivations on ℓ-Rings:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eExamples and Basic Properties\u003c\/li\u003e\n\u003cli\u003eƒ-Ring and Its Generalizations\u003c\/li\u003e\n\u003cli\u003eMatrix ℓ-Rings\u003c\/li\u003e\n\u003cli\u003eKernel of a Positive Derivation\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eSome Topics on Lattice-Ordered Rings:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eRecognition of Matrix ℓ-Rings with the Entrywise Order\u003c\/li\u003e\n\u003cli\u003ePositive Cycles\u003c\/li\u003e\n\u003cli\u003eNonzero ƒ-Eelements in ℓ-Rings\u003c\/li\u003e\n\u003cli\u003eQuotient Rings of Lattice-Ordered Ore Domains\u003c\/li\u003e\n\u003cli\u003eMatrix ℓ-Algebras Over Totally Ordered Integral Domains\u003c\/li\u003e\n\u003cli\u003e\n\u003ci\u003ed\u003c\/i\u003e-Elements That are Not Positive\u003c\/li\u003e\n\u003cli\u003eLattice-Ordered Triangular Matrix Algebras\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eℓ-Ideals of ℓ-Unital Lattice-Ordered Rings:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eMaximal ℓ-Ideals\u003c\/li\u003e\n\u003cli\u003eℓ-Ideals in commutative ℓ-Unital ℓ-Rings\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduate students in algebra and number theory.\u003cbr\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eThe book includes new material such as positive derivations on lattice-ordered rings, lattice-ordered triangular matrix algebras\u003c\/li\u003e\n\u003cli\u003eMore details are provided in proofs of the results in the book for beginners to understand the text\u003c\/li\u003e\n\u003cli\u003eThe book presents new research ideas, methods and topics suitable to advanced undergraduate students and master students\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47143741456624,"sku":"9789814571449","price":17.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814571449_p0.jpg?v=1763691116","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814571449","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}