ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632083

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The purpose of this survey is two-fold, primarily to compile a selection of rings and ring constructions which distinguish radical theoretical properties of rings. This will be achieved mainly by the secondary aim which is to localize the position of most of the known radicals, in particular thatJϕ≠B(the existence of a simple primitive ring without non-zero idempotent),K≠Kp(the existence of a ringAwith zero total such that for every prime idealP(≠A) the total ofA/Pis not zero) and that(Veldsman's left superprime radical is properly contained in Olson's uniformly strongly prime radical).

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632084

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We study commutativity of prime ringsRsuch thatd(S) is central, wheredis a non-zero derivation andSa suitably-chosen subset ofR.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632085

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

This paper is primarily a survey of the results on essential covers of radical classes of rings. Some problems are posed, and some new results are presented.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632086

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Right cones are semigroups for which the lattice of right ideals is a chain and a left cancellation law holds; valuation rings, the cones of ordered groups, and initial segments of ordinal numbers are examples. Two such cones are associated if they have isoniorphic lattices of right ideals so that ideals, prime ideals, and completely prime ideals correspond to each other. A list of problems is discussed. In Proposition 3.11 it is proved that the canonical mapping from a right invariant right chain domainRonto the associated right holoid can be extended to a valuation from the skew fieldQ(R)of quotients ofRonto an ordered group if and only ifJa⊆aJfor alla∈RandJ=J(R), the Jacobson radical ofR.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632087

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this article the concepts ofk-quasi-regularity andk-primitivity are defined forK-algebras,Ka commutative ring with identity, 0 ≠kεK.It is then shown that a special radical is obtained and thatk-primitive algebras can be characterized in terms of dense algebras of linear transformations.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632088

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We investigate the role played by torsion properties in determining whether or not a commutative quasiregular ring has its additive and circle composition (or adjoint) groups isomorphic. We clarify and extend some results for nil rings, showing, in particular, that an arbitrary torsion nil ring has the isomorphic groups property if and only if the components from its primary decomposition intop-rings do too.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632089

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Some radicals connected with atoms of the lattice of all special radicals of associative rings are studied.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632090

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

An idealAof a ringRis called a good ideal if the coset productr1r2+Aof any two cosetsr1+Aandr2+AofAin the factor ringR/Aequals their set product (r1+A) º (r2+A): = {(r1+a)(r2+a2):a1,a2εA}. Good ideals were introduced in [3] to give a characterization of regular right duo rings. We characterize the good ideals of blocked triangular matrix rings over commutative principal ideal rings and show that the conditionAºA=Ais sufficient forAto be a good ideal in this class of matrix rings, none of which are right duo. It is not known whether good ideals in a base ring carries over to good ideals in complete matrix rings over the base ring. Our characterization shows that this phenomenon occurs indeed for complete matrix rings of certain sizes if the base ring is a blocked triangular matrix ring over a commutative principal ideal ring.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632091

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

This paper is based on an expository talk given at the International Conference on Radicals and Rings ICOR 97. Our aim is not to give a comprehensive survey of the subject. We rather wish to present some selected results and on their basis to analyze the development of radical theory of near-rings, emphasizing the role of non-zerosymmetric near-rings. Besides we present some new results on Jacobson type radicals of non-zerosymmetric near-rings.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632092

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor