摘要:

It is shown that (concretely) Cartesian closed topological hulls can be characterized as injective hulls in a rather natural setting. The characterization of locale hulls as injective hulls in the category of (meet-) semilattices by Bruns & Lakser and Born & Kimura constitutes a special case.

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632116

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632117

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

A complex is introduced which is the grade-theoretic analogue of the COUSIN complex of GROTHENDIECK and SHARP. Some applications are indicated to commutative algebra and geometry.

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632118

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Let R be a noetherian ring, and denote the full subcategories of R-modules L such that Exti(E,L)=0 for all injective R-modules E for 1⋚i⋚n and O⋚i⋚n by Cn, and C′nrespectively. Then LεCn, if and only if every injective resolution of L is an injective resolvent of the nth cosyzygy. In this case, L is not injective if and only if its injective dimension is greater than n. If LεC′nand idN⋚n. then Hom(N,L)=0 for all R-modules N. As an application, let Knbe the nth syzygy of an injective resolvent of the nth cosyzygy of an R-module N, then there exists a homomorphism φ:N → K such that ((φ,iN), Kn• E(N)) and (φ,Kn) are preenvelopes of N for Csand C′srespectively, for s≥n. If the global dimension of R is at most 2, then C′1is reflective in the category of R-modules.

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632119

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In this paper we give a survey of a few selected results on non-commutative K1-ull rings in the sense of L. Le Bruyn, P. Wauters and the author. These rings are called Ω-Krull rings.

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632120

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

An improved bound is given for the index of nil-potency of a finitely generated nil ring of index n in terms of the index of nilpotency of the ideal generated by Tmwhere m = [n/2] and T is a m-subset of the set of generators. If m = 3 it is proved that T10is contained in an ideal generated by twenty-seven cubes and this is applied to get bounds for the index of nilpotency of a finitely generated nil ring of index 6 or 7, bounds which are less than one hundredth of the bounds we obtained in a previous paper.

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632121

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Let k be a field and suppose ζnis a primitive n-th root of unity contained in k. We denote by Sr(k) = H2(Gk,Cx) the Schur multiplier of k. We observe: If the n-part of Sr(k) is trivial, then every element of order n in the Brauer group Br(k) can be represented as a cyclic algebra of the form

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632122

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

It is shown that if R is a GCD domain which is not Bézout, then there exist pure-injective R-modules which are not RD-injective.

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632123

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The aim of this note is to extend the results of tilted artinian algebras [2, 4, 3, 1] to orders. Some of the proofs carry over almost unchanged from the artinian case to the case of orders: others need considerable alteration—in particular the results on global dimensions. For the convenience of the reader we shall give complete proofs here—some are taken directly from [2].

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632124

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The concept of a semiring is introduced as a semilattice analogue of a semiring of sets. A detailed study of its embeddability into r-complete Boolean algebras is carried out. Some of its properties which are important from the standpoint of Measure Theory are elucidated. A representation of a semiring by a Semiring of sets is derived. A relation to implicative BCK-algebras is also mentioned.

ISSN:1607-3606    

DOI:10.1080/16073606.1986.9632125

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor