摘要:

This paper deals with two themes involving the going down (GD) behavior of the overrings of a domain R. First, as illustrated by several results in [3] and [4], hypotheses about GD often replace stronger assumptions about flatness or one-dimensionality in sets of conditions implying that R is Prüfer. Second, as shown by the two-dimensional example in [4]. Remarks (iii)], some sort of finiteness condition is required in conjunction with GD hypotheses in order for R to be Prüfer.

ISSN:0092-7872    

DOI:10.1080/00927877408548715

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

Given a cotriple 𝔾 = (G, ε, δ) on a categoryXand a functor E:XOpp→Ainto an abelian categoryA, there exists the cohomology theory of Barr and Beck: Hn(X, E) ε |A| (n ≥ 0, X ε |X|), ([1], p.249). Almost all the important cohomology theories in mathematics have been shown to be special instances of such a general theory (see [1], [2] and [3]). Usually E arises from an abelian group object Y inXin the following manner: it is the contravariant functor fromXinto the categoryAbof abelian groups that associates to each object X inXthe abelian groupX(X, Y) of maps from X to Y. In such a situation we shall write Hn(X, Y)𝔾instead of Hn(X, E)G. Barr and Beck [2] have shown that the Eilenberg-MacLane cohomology groups H̄n(π, A), n ≥ 2, can be re-captured as follows. One considers the free group cotriple 𝔾′ on the categoryGpsof groups, which induces in a natural manner a cotriple 𝔾 on the category (Gps, π) of groups over a fixed group π.

ISSN:0092-7872    

DOI:10.1080/00927877408548716

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

With a Weyl group W and a positive integer p are associated p-linkage classes of weights [4,13]. Small deformations of such classes by elements of W are introduced here. These lead in turn to certain polynomials in p with highest term pm, m = number of positive roots (one polynomial for each conjugacy class of W), which are written down explicitly for types A1, A2, B2. These polynomials give (for each prime p) the degrees of the various large series of irreducible characters of the corresponding Chevalley group over the field of p elements. Indeed, the formal behavior of weights appears to reflect the actual behavior of the characters under reduction modulo p.

ISSN:0092-7872    

DOI:10.1080/00927877408548717

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

Ist K ein kommutativer Körper und A eine assoziative Algebra über K, so interessiert man sich für die Gesamtheit aller endlichdimensionalen Darstellungen von A über K, d.h. für den Halbring der Charaktere auf A/K. Charaktere sind spezielle K-lineare, zentrale Funktionen auf A mit Werten in K. In dieser Bemerkung sollen für Grundkörper K der Charakteristik Null die Charaktere unter den K-wertigen K-linearen zentralen Funktionen auf A durch eine einfache Funktionalgleichung gekennzeichnet werden. Handelt es sich bei A um die Gruppenalgebra K[G] einer beliebigen Gruppe G, so liefert dies eine schon auf G formulierbare Kennzeichnung der Gruppencharaktere unter den Klassenfunktionen auf G. Der hier aufgerollte Formalismus, der der Aufmerksamkeit bisher entgangen zu sein scheint, ist elementar und kommt ohne Induktionsprozesse sowie ohne verallgemeinerte Charaktere aus.

ISSN:0092-7872    

DOI:10.1080/00927877408548718

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

The irreducible representations of the generic algebra of a Chevalley group with Borel subgroup B correspond to the irreducible representations of G that are constituents of the induced representation. The few explicitly constructed representations of the generic algebra have been obtained by “lifting” representations of the corresponding Weyl group W. For example, in [2] representations were constructed that specialize to the linear representations, the reflection representation and its compounds, and, in the dihedral case, all the representations of W (see also [6]).

ISSN:0092-7872    

DOI:10.1080/00927877408548719

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

It is a well-known result that the direct sum of any family of injective modules over a Noetherian ring is injective. Conversely, ifAis a ring with the property that the direct sum of any family of injective modules is injective H. Bass [1] has shown thatAis Noetherian. The object of the present paper is to give necessary and sufficient conditions for the direct sum of a given family of modules over an arbitrary ring to be injective.

ISSN:0092-7872    

DOI:10.1080/00927877408548720

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor