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Titlebook: Algebra; Thomas W. Hungerford Textbook 1974 Springer-Verlag New York, Inc. 1974 Adjoint functor.Coproduct.Galois theory.algebra.field.fini

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Linear Algebra,momorphisms of (finitely generated) free modules (in particular, linear transformations of finite dimensional vector spaces). There is a crucial relationship between such homomorphisms and matrices (Section 1). The investigation of the connection between two matrices that represent the same homomorp
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The Structure of Rings,pplication, complete structure theorems are available only for certain classes of rings. The basic method for determining such a class of rings might be described intuitively as follows. One singles out an “undesirable” property . that satisfies certain conditions, in particular, that every ring has
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Categories,k of Eilenberg-Mac-Lane in algebraic topology in the 1940s. It was soon apparent that these concepts had far wider applications. Many different mathematical topics may be interpreted in terms of categories so that the techniques and theorems of the theory of categories may be applied to these topics
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Algebra978-1-4612-6101-8Series ISSN 0072-5285 Series E-ISSN 2197-5612
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Commutative Rings and Modules,d prime ideals (Section 2), both of which play a central role in the study of commutative rings. Actually no commutativity restrictions are made in Section 1 since this material is also essential in the study of arbitrary rings (Chapter IX).
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Eman M. M. Zayed,Ola H. Abdelbarlly the same are said to be isomorphic. Ideally the goal in studying groups is to classify all groups up to isomorphism, which in practice means finding necessary and sufficient conditions for two groups to be isomorphic. At present there is little hope of classifying arbitrary groups. But it is pos
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