摘要:

A lattice is called groupable provided it can be endowed with the structure of anl-group (lattice ordered group). The primary objective of this paper is to introduce an order theoretic property of groupable lattices which implies that all associatedl-groups are subdirect products of totally ordered groups. This is an analog to Iwasawa's well-known result which asserts that a conditionally completel-group is abelian. A secondary objective is to outline a general method for identifying classes ofl-groups determined by order theoretic properties.

ISSN:0092-7872    

DOI:10.1080/00927879508825497

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

An abelian group G is said to be E-finitely generated (respectively, E-cyclic) if it is finitely generated (resp., cyclic) as a module over its endomorphism ring E. In this paper we refine a theorem of Reid [5] cUid apply the result to settle a question of some years standing concerning infinitely gen¬erated groups. We also determine the structure of torsion-free groups of finite rank for which Q ⊗zis a progenerator over Q ⊗zE

ISSN:0092-7872    

DOI:10.1080/00927879508825498

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

All isomorphisms between comutative semigroup algebras K[S] and K[T] are found when K is a field and S, T have two generators subject to a single homogeneous defining relation

ISSN:0092-7872    

DOI:10.1080/00927879508825499

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

In this paper we study loop algebras of code loops in the modular case and, in particular, we show that code loops are determined by their loop algebras over the field with two elements. Actually, many of our results hold for a wider family of loopsLwhich we introduce in the second section.

ISSN:0092-7872    

DOI:10.1080/00927879508825500

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

This paper presents two axiomatic description of infinite root systems in a base free way. In 1982, Moody and Yokonuma proposed a set of axioms for infinite root systems. These axioms are not general enough to capture all objects that one would intuitively recognize as root systems. The Moody and Yokonuma axioms are expanded to obta n the geometric root system axioms, which capture objects missed by the Moody and Yokonuma axioms. As well, a new set of axioms, rational root systems, is presented. Unlike other axiom systems for root systems, rational root systems are independent of any assumptions about the underlying field. Another system of axioms, root data, has been developed by Moody and Pianzola. The three axiom systems are shown to be 'equivalent.

ISSN:0092-7872    

DOI:10.1080/00927879508825501

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

Let R be a commutative and noetherian ring. It is known tht if R is local with maximal ideal M and F is a flat R-module, then the Hausdorff completion F of F with the M-adic topology is flat. We show that if we assume that the Krull dimension of R is finite, then for any ideal I C R, the Hausdorff completion F* of a flat module F with the I-adic topology is flat. Furthermore, for a flat module F over such R, there is a largest ideal I such that F is Hausdorff and complete with the I-adic topology. For this I, the flat R/I-module F/IF will not be Hausdorff and complete with respect to the topology defined by any non-zero ideal of R/I. As a tool in proving the above, we will show that when R has finite Krull dimension, the I-adic Hausdorff completion of a minimal pure injective resolution of a flat module F is a minimal pure injective resolution of its completion F*. Then it will be shown that flat modules behave like finitely generated modules in the sense that on F* the I-adic and the completion topologies coincide, so F* is I-adically complete.

ISSN:0092-7872    

DOI:10.1080/00927879508825502

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879508825503

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879508825504

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

An integral domain D with quotient field K is defined to be agreeable if for each fractional ideal F of D[X] with F C K[X] there exists 0 = s ε D with sF C D[X]. D is agreeable ⇔ D satisfies property (*) (for 0 ^ f(X) G K[X], there exists 0 = s ε D so that f(X)g(X) ε D[X] for g(X) ε K[X] implies that sg(X) ε D[X]) & D[X] is an almost principal domain, i.e., for each nonzero ideal I of D[X] with IK[X] = K[X], there exists f(X) ε I and 0 = s ε D with sI C (f(X)). If D is Noetherian or integrally closed, then D is agreeable. A number of other characterizations of agreeable domains are given as are a number of stability properties. For example, if D is agreeable, so is ⋂αDPαand for a pair of domains D⊆D′ with a [DD:′]≠0, D is agreeable⇔D′ is agreeable. Results on agreeable domains are used to give an alternative treatment of Querre's characterization of divisorial ideals in integrally closed polynomial rings. Finally, the various characterizations of D being agreeable are considered for polynomial rings in several variables.

ISSN:0092-7872    

DOI:10.1080/00927879508825505

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

R denotes a commutative ring. After Bass[B], a ring R is perfect in case every module has a projective cover. A ring R is a maxringprovided that every nonzero i2-module has a maximal submodule. Bass characterized perfect rings as semilocal rings with T-nilpotent Jacobson radical J, and showed they are max rings. Moreover, Bass proved that R is perfect iff R satisfies the dec on principal ideals. Using Bass' theorems, the Hamsher-Koifman ([H],[K]) characterization of max R (see (3) ⇔(4) below), and the characterization of max R by the author via subdirectly irreducible quasi-injective R-modules, we obtain.

ISSN:0092-7872    

DOI:10.1080/00927879508825506

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor