摘要:

LetRbe a commutative ring with identity. ConsiderRas a simple graph with vertices elements ofRwhere any two distinct elements x, y ϵ R are adjacent if and only if xy = 0. Beck [2] conjectured that ℵ(R) =c1(R), for all colorings R. Anderson and Naseer [1] provided a counter example to the conjecture i.e., gave an example of a non-chromatic ring. This paper generalizes the example and gives a large class of non-chromatic rings [Theorem 1.1]• A detailed analysis of the graph of these rings is also provided.

ISSN:0092-7872    

DOI:10.1080/00927879808826143

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We construct a rigid irreflexive monoid with right ACC1which is not the free product of its group of units and any submonoid. This example disproves a conjecture of Cohn's.

ISSN:0092-7872    

DOI:10.1080/00927879808826144

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826146

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

The right alternative law implies the left alternative law in loop rings of characteristic other than 2. We also exhibit a loop which fails to be a right Bol loop, even though its characteristic 2 loop rings are right alternative.

ISSN:0092-7872    

DOI:10.1080/00927879808826147

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

A four-dimensional real algebra 𝔄 is left ¢-associative (with rapect to ℭ) if 𝔄 is a bimodule with respect to a subalgebra ℭ isomorphic to the complex numbers, and c(AB) = (cA)B for all A, B in 𝔄 and all c in ℭ. We reduce the division algebra condition for such algebras to a question about a single-variable quartic, classify the division algebras, and show they all have nullity one. We determine the derivation algebras and find intersections with other classes of algebras. Right ¢-associative algebras are considered via the opposite algebra.

ISSN:0092-7872    

DOI:10.1080/00927879808826148

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

The structure of the semigroupSis investigated when the semigroup ringRSadmits a compact topology. It is proved that, in case of the semisimple semigroupS, the ”last” principal factors of S have finitely many of right or left ideals. It is shown that it is not true for other factors.

ISSN:0092-7872    

DOI:10.1080/00927879808826149

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826150

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826151

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826152

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826153

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor