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The book generalizes the well-known regularity of ring elements to regularity of homomorphisms in module categories, and further to regularity of morphisms in any category. Regular homomorphisms are characterized in terms of decompositions of domain and codomain, and numerous other results are presented. While the theory is well developed in module categories many questions remain about generalizations and extensions to other categories. The book only requires the knowledge of a basic course in modern algebra. It is written clearly, with great detail, and is accessible to students and researchers alike.
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Recensione
From the reviews:
“This book is dedicated to generalizations of regularity for an Abelian group ... . contains an excellent and detailed exposition of results on all types of regularity in Hom with consequences for modules and rings. It is accessible, with all necessary definitions and proofs, contains also a series of instructive examples. ... interest both for students and specialists.” (A. I. Kashu, Zentralblatt MATH, Vol. 1169, 2009)Contenuti
Preface.- 1. Notation and background.- 2. Regular hmomorphisms.- 3. Indecomposable modules.- 4. Regularity in modules.- 5. Regularity in HomR(A,M) as one-sided module.- 6. Relative regularity: U-regularity and semiregularity.- 7. Reg(A,M) and other substructures of Hom.- 8. Regularity in homomorphism groups of abelian groups.- 9. Regularity in categories.- Bibliography.- Index.
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Regularity and Substructures of Hom (Frontiers in Mathematics)
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Condizione: Fine. 179 pp., Paperback, fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Codice articolo ZB1281036
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Regularity and Substructures of Hom.
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Basel, Birkhäuser., 2009
ISBN 10: 3764399899
ISBN 13: 9783764399894
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XV, 164 p. Softcover. Versand aus Deutschland / We dispatch from Germany via Air Mail. Einband bestoßen, daher Mängelexemplar gestempelt, sonst sehr guter Zustand. Imperfect copy due to slightly bumped cover, apart from this in very good condition. Stamped. Stamped. Frontiers in Mathematics Sprache: Englisch. Codice articolo 6126DB
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Regularity and Substructures of Hom (Paperback)
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Birkhauser Verlag AG, Basel, 2009
ISBN 10: 3764399899
ISBN 13: 9783764399894
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Paperback. Condizione: new. Paperback. Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not ?nite-dimensional ([8, page 155], [32, page V]). Von Neumann proved ([32, Theorem 14. 1, page 208], [8, page 162]): Every continuous geometry is isomorphic to the lattice of right ideals of some regular ring. The book of K. R. Goodearl ([14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ([27], [31], [15]). In abelian group theory the interest lay in determining those groups whose endomorphism rings were regular or had related properties ([11, Section 112], [29], [30], [12], [13], [24]). An interesting feature was introduced by Brown and McCoy ([4]) who showed that every ring contains a unique largest ideal, all of whose elements are regular elements of the ring. In all these studies it was clear that regularity was intimately related to direct sum decompositions. Ware and Zelmanowitz ([35], [37]) de?ned regularity in modules and studied the structure of regular modules. Nicholson ([26]) generalized the notion and theory of regular modules. In this purely algebraic monograph we study a generalization of regularity to the homomorphism group of two modules which was introduced by the ?rst author ([19]). Little background is needed and the text is accessible to students with an exposure to standard modern algebra. In the following, Risaringwith1,and A, M are right unital R-modules. Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). Goodearl ([14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ([27], [31], [15]). Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9783764399894
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Regularity and Substructures of Hom (Frontiers in Mathematics)
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not nite-dimensional ([8, page 155], [32, page V]). Von Neumann proved ([32, Theorem 14. 1, page 208], [8, page 162]): Every continuous geometry is isomorphic to the lattice of right ideals of some regular ring. The book of K. R. Goodearl ([14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ([27], [31], [15]). In abelian group theory the interest lay in determining those groups whose endomorphism rings were regular or had related properties ([11, Section 112], [29], [30], [12], [13], [24]). An interesting feature was introduced by Brown and McCoy ([4]) who showed that every ring contains a unique largest ideal, all of whose elements are regular elements of the ring. In all these studies it was clear that regularity was intimately related to direct sum decompositions. Ware and Zelmanowitz ([35], [37]) de ned regularity in modules and studied the structure of regular modules. Nicholson ([26]) generalized the notion and theory of regular modules. In this purely algebraic monograph we study a generalization of regularity to the homomorphism group of two modules which was introduced by the rst author ([19]). Little background is needed and the text is accessible to students with an exposure to standard modern algebra. In the following, Risaringwith1,and A, M are right unital R-modules. 184 pp. Englisch. Codice articolo 9783764399894
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