摘要:

Weakly special classes of hemirings are defined and properties are obtained which have the flavour of those in ring theory. A condition is given which yields an equivalence to the definition of a special class. The radical generated by the class of prime hemirings is characterized as the intersection of a new collection of ideals and several questions are posed.

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631678

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Equiprime near-rings, which generalize the concept of prime-ness in rings, were defined by the present authors, together with S. Veldsman. This concept was shown in subsequent work to lead to a very satisfactory theory of special radicals for near-rings. In the current paper, we define equiprimeN-groups for a near-ringN. It is shown that an idealAofNis equiprime if and only if it is the annihilator of an equiprime TV-groupG.Special classes of near-ring modules are defined, and a module-theoretic characterization of special radicals of near-rings is established, similar to that given by Andrunakievich and Rjabuhin for special radicals of rings.

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631679

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Letmbe a positive cardinal. We denote by Pr(m) (resp.Pt(m)) the class of all ringsRfor whichmis the least cardinal such that all nonzero elements ofRpossess right (resp. left) insulators of cardinality less than m + 1. We also setPr(m) = Un≤ m Pr(n). The classes Pr(m),>m0, partition the class of all prime rings. Various descriptions of these classes are obtained. In particular ifmis regular thenPr(m) contains just those ringsRsuch thatt(R) = 0 for all proper torsion preradicalston Mod -Rwhose torsion classes are closed under direct products of fewer than m modules. Examples are provided which show thatPr(m) is non-empty for all m > 0 and which partially answer the question: for which cardinalsm,nisPr(m) ∩Pt(n) nonempty?

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631680

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

LetXandYbe normed linear spaces. A linear operatorT:D(T) ⊂X→Yis called anF-operator if its adjointT′:D(T) ⊂Y′→D(T)' is aφ+-operator, i.e. has closed range and finite dimensional-kernel. Characterisations of anF_-operatorTare obtained in the general case and in the case whenTis closable. Unbounded strictly cosingular operators are defined and shown to belong to the class ofF_ -admissible pertubations wheneverYis complete.

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631681

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A new definition of the hypergraph functor from the category TOP(L) ofL-fuzzy topological spaces to TOP is given which avoids the strictly less-than relation onL. ForLa complete latticewith enoughprimes it will have all the earlier properties of the case whenLis a complete chain. WithLa continuous lattice, the functor ωLwhich replaces the topology of a topological space by theL-topology consisting of all Scott continuous functions is discussed and some sufficient and necessary conditions for anL-fuzzy space to be in ωL(TOP) are extended fromLbeing the unit interval. Under this new approach the link between the hypergraph functor and the functor ωLis preserved forLa distributive continuous lattice, i.e. a continuous lattice with enough primes.

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631682

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The concept of ultra-universal algebras in varieties is generalized to models of first order theories. Characterizations of theories which have ulta-universal models are found and general examples of ultra-universal models are investigated. In particular we show that a theory has an ultra-universal model iff it is consistent and its class of models satisfies the joint embedding property.

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631683

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

In this paper we determine the exponents α0, α, β0, β for which the Hardy inequality

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631684

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

It is shown that anyR[G]-ideal (-submodule) ofR(G)is contained in anR[G]-ideal (-submodule) of the formR(G)whereLis a left ideal (leftR-subgroup) of the near-ringR.For a connectedR-moduleNanR[G]-module structure is denned onN(G)such that if the near-ringRis 1-primitive onRNthenN(GM)is a faithful monogenicR[G]-module. Furthermore it is shown that ifNis a connectedR-module then there is a monomorphism fromEndRNintoEndR[G]N[G](as monoids). Finally a relationship is given between theJ½- andJ0-radical of the near-ringR.

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631685

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Matrix near-rings and group near-rings were defined in [3] and [2], respectively. It is shown that there is an epimorphism from the group near-ring over the matrix near-ring onto the matrix near-ring over the group near-ring.

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631686

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1992.9631687

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor