Titlebook: Algebra; Some Recent Advances I. B. S. Passi Book 1999 Hindustan Book Agency (India) and Indian National Science Academy 1999 Area.Volume.a

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Jordan Decomposition,o semisimple and nilpotent parts) for matrices over perfect fields is perhaps less well known, though very useful in many areas and closely related to the canonical form. This Jordan decomposition extends readily to elements of group algebras over perfect fields. During the past decade or so there h

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Galois Cohomology of Classical Groups,honological dimension 2. Number fields are examples of such fields. We begin by describing a well-known classification theorem for quadratic forms over number fields in terms of the so-called classical invariants (§ 2). We explain in § 3 how this classification leads to Hasse principle for principal

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Alternative Loop Rings and Related Topics,, see Definition 3.1). The . of . over . was introduced in 1944 by R.H. Bruck (1944) as a means to obtain a family of examples of nonassociative algebras and is defined in a way similar to that of a group algebra; i.e., as the free A-module with basis ., with a multiplication induced distributively

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,-values at Zero and the Galois Structure of Global Units,and the values at zero of Artin .-functions. The algebraic ingredients come from integral representation theory, the ones from number theory include the Main Conjecture of Iwasawa theory. In fact, the discussion of recently defined invariants which go along with the unit group seems to propose possi

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On Subgroups Determined by Ideals of an Integral Group Ring,iven by ∈ (Σ....) = Σ.... ∈ ., .. ∈ ., and it is generated as a free .-module by the elements . 1, ., .. For . 1, let ..(.) denote the .th associative power of .(.). For an ideal . of ., let G ∩ (1 + .) = {. -1 ∈ .}. Observe that for ., . ∈ . ∩ (1 + .), . ∈ .,. and . which imply that . ∩(1 + .) is a

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2297-0215 Overview: 978-3-0348-9998-7978-3-0348-9996-3Series ISSN 2297-0215 Series E-ISSN 2297-024X