Irreducible restriction and zeros of characters

Let be a finite group, let be normal in and suppose that is an irreducible complex character of . Then is not irreducible if and only if vanishes on some coset of in .

     

On the restriction of Deligne-Lusztig characters

We study the multiplicities of Deligne-Lusztig characters upon restriction from a finite reductive group to a finite reductive subgroup. The result is a qualitative formula for the growth of multiplicities in terms of complexity. For restrictions from to we get exact multiplicities.

     

Injective Rings

The purpose of this article is to determine the injective objects in some complete categories of rings. All rings are assumed to have identities and it is assumed that the homomorphisms preserve these identities. We recall that an object Q in a category is called injective if for every diagram where A′ → A is a monomorphism, there is a map A → Q making the triangle commute. The zero ring belongs to all the categories discussed and it is easy to see that it is an injective object. For the categories of commutative rings, strongly regular and commutative regular rings we show that the zero ring is the only injective by using the fact that an injective object must be a retract of any extension. We include in this section the known results which characterize the injective rings and p-rings. The second part of the paper discusses injectivity with respect to regular monomorphisms. Some necessary categorical background is given and it is then shown that results analagous with those of the first section hold (including the known Boolean and p-ring cases). In an abelian category all monomorphisms are regular, so in the study of the injective objects, for example injective modules, there are not two separate cases.     

Injective minimal modules

Minimal modules over a ring with infinite center are studied. A characterization of rings R with center C, admitting minimal modules with C-torsion, is obtained. Minimal injective modules over a commutative ring are described.Translated fromAlgebra i Logika, Vol. 33, No. 2, pp. 211-226, March-April, 1994.     

Injective choice functions

The present paper is concerned with a combinatorial question called the “marriage problem.”. A criterion will be proved for the existence of an injective choice function of families with at most finitely many infinite members and a generalization of a theorem of H. A. Jung and R. Rado. We give a new proof of a theorem of J. Folkman.     

Main Injective Rings

We refer to those injective modules that determine every left exact preradical and that we called main injective modules in a preceding article, and we consider left main injective rings, which as left modules are main injective modules. We prove some properties of these rings, and we characterize QF-rings as those rings which are left and right main injective.     

内射模的t－平坦性

设Ｒ为环，ｔ是左Ｒ－模范畴的一个遗传挠理论．文中证明了下述各点等价：（１）每个内射左Ｒ－模是ｔ－平坦的；（２）每个ｔ－有限表现左Ｒ－模的内射包络是ｔ－平坦的；（３）每个ｔ－有限表现左Ｒ－模是自由Ｒ－模的子模；（４）每个ｔ－有限表现左Ｒ－模是自反的且其对偶模是Ｈ－有限生成的．     

内射拓扑分子格

本文证明了任给T_O拓扑分子格(L,η),以下三条等价:(1)(L,η)为正则内射拓扑分子格;(2)L为完备集环且其完备余素元集ht(L)形成一连续格,余拓扑η为该连续格ht(L)上的Scott闭集格;(3)存在T_O内射拓扑空间(X,Τ),(L,η)同胚于(P(X),Τ~c)在拓扑分子格范畴中的Sober化。此外,还给出了正则内射拓扑分子格、(一般)内射拓扑分子格以及正则内射分子格的一般结构。作为应用,重新证明了有指数元的拓扑分子格的结构。     

The Injective Leavitt Complex

For a finite quiver Q without sinks, we consider the corresponding finite dimensional algebra A with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of injective A-modules. We call such a generator the injective Leavitt complex of Q. This terminology is justified by the following result: the differential graded endomorphism algebra of the injective Leavitt complex of Q is quasi-isomorphic to the Leavitt path algebra of Q. Here, the Leavitt path algebra is naturally \(\mathbb {Z}\)-graded and viewed as a differential graded algebra with trivial differential.     

Injective Hulls of Quantale-Enriched Multicategories

Applied Categorical Structures - In this communication we generalize some recent results of Rump to categories enriched in a commutative quantale V. Using these results, we show that every...     

Injective Hulls in POSV

We determine the injective objects and hulls in the category POS_V. This category is similar to the one of join semilattices but contains all partially ordered sets. The results of this paper have applications, for instance, in the theory of (generalized) ultrametric spaces.