ISSN:0092-7872    

DOI:10.1080/00927879208824435

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824436

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824437

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824438

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Let AlB be an H—extension for a finite Hopf algebra H. First we characterize such Hopf extensions that are Frobenius extensions. Second we will give some characterizations of Hopf Galois extensions, which extend the result of Cohen-Fishmann-Montgomery

ISSN:0092-7872    

DOI:10.1080/00927879208824439

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

A notion of generalized inverse extending that of Moore—Penrose inverse for continuous linear operators between Hilbert spaces and that of group inverse for elements of an associative algebra is defined in any Jordan triple system (J, P). An element a∈J has a (unique) generalized inverse if and only if it is strongly regular, i.e., a∈P(a)2J. A Jordan triple system J is strongly regular if and only if it is von Neumann regular and has no nonzero nilpotent elements. Generalized inverses have properties similar to those of the invertible elements in unital Jordan algebras. With a suitable notion of strong associativity, for a strongly regular element a∈J with generalized inverse b the subtriple generated by {a, b} is strongly associative

ISSN:0092-7872    

DOI:10.1080/00927879208824440

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824441

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Let D be a Dedekind domain. D is a half factorial domain (HFD) if for any irreducible elementsof D the equalityimplies that s = t. D is a congruence half factorial domain (CHFD) of order r>1 if the same equality implies that s = t (mod r). In this paper we expand upon many of the known results for HFDs and CHFDs (see [6] and [7]) as well as introduce the following new class of domains: if k≥1 is a positive integer then D is a k—ha1f factorial domain (k—HFD) if s Skin the previous equality implies that s = t. In section I we explore the interrelationship of the HFD, CHFD, and k—HFD properties and offer a method for constructing examples of k—HFDs and CHFDs by viewing the class group of the given domain as a direct summand. In particular, we show in section I that the HFD, CHFD, and k—HFD properties are equivalent for rings of algebraic integers. In section II we extend the results of section I by constructing examples of Dedekind domains which are both CHFD and k—HFD but not HFD. In section In we explore the k-HFD property in detail when the class group of D is a torsion group. Finally in section IV we study the HFD, CHFD, and k—HFD properties in Dedekind domains with class group 11.

ISSN:0092-7872    

DOI:10.1080/00927879208824442

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

LetAbe a finite dimensional commutative semisimple algebra over a fieldkand letVbe a finitely generatedA—module. In previous work the author examined the action of the general linear group GLA(V) on the Grassmannians ofk—subspaces ofV. The present paper examines the structure of the orbits in greater detail, in particular by working out the structure of the stabilizers in each of the cases when dimkA≤3. From an algebraic point of view the most interesting situation occurs forAa cubic extension field ofk

ISSN:0092-7872    

DOI:10.1080/00927879208824443

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824444

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor