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

镶嵌细工

Databases Theory and Applicationso 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

极少

Xiu Susie Fang,Xianzhi Wang,Quan Z. Shenghonological 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

minion

Databases Theory and Applications book by Sehgal (1993) while a survey paper by Jespers contains additional very recent results. Both of these sources contain results on central units (in fact, Jespers devotes a chapter to the topic), but our work complements theirs in two ways. Firstly, we describe some results contained in papers

Cabinet

Supriya,Siuly,Hua Wang,Yanchun Zhang, 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

Conquest

Databases Theory and Applicationsand 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

Modify

Lei Li,Xiaofang Zhou,Kevin Zhengiven 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

Consensus

Lei Li,Xiaofang Zhou,Kevin Zhenga finite group, whose character is real, either descends to a real representation or can be extended to a representation of the group over the real quaternion algebra. The simplest example where the latter phenomenon holds is the standard 2-dimensional complex representation of the group of integral

BUOY

Apogee

On Abelian Difference Sets,(1990), Jungnickel (1992., .Pott (1995), Jungnickel and Schmidt (1997), and Davis and Jedwab (1996). Standard references for difference sets are Baumert (1971), Beth .. (1998), and Lander (1983). This article presents a flavour of the subject, by discussing some selected topics.

vocation

Around Automorphisms of Relatively Free Groups,The bibliography at the end is neither claimed to be exhaustive, nor it is necessarily connected with a reference in the text. I include it as 1 see it revolves . the concepts emerging from the investigation of automorphisms of free groups. The interested reader may find it useful to browse over the list occasionally.