摘要:

Letk,nbe positive integersGa residually finite group such thatisn-Engel for any. We prove that γk(G) is locally nilpotent. Fork= 1 this is a well-known result of J. Wilson.

ISSN:0092-7872    

DOI:10.1080/00927879908826540

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

The Asymptotic Theory of ideals originated with the investigation in noetherian ringAof the Samuel numbers ⊢I(J) and [wbar]I(J) associ-ated to each pair (I, J) of nonnilpotent ideals having the same radical where, the limit being reached from below and. The number [wbar]I(J) is defined in a symetric situation. As an answer of a question raised by Samuel, Nagata has shown that the set of deviationsis bounded. Here we extend these numbers to pairs (f,g), wheref= (In) andg= (Jn) are filtrations onA, as follows:, wheref(r) is filtration (Inr). We prove in particular that iffandgare separated, nonnilpotent, stronglyAPfiltrations and suchthen the deviation sequenceis bounded in R+. A similar study is done concerning the sequenceandbf(g) = ∞ if the last set is empty.

ISSN:0092-7872    

DOI:10.1080/00927879908826541

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

This paper determines the Z-module structure of the homoge-neous submodules of degree ≤ 6 of the free semialternative ring over Z on one generator. There are no elements of finite order in degree ≤ 4. In degree 5 the torsion subgroup is isomorphic to Z2, and in degree 6 the torsion subgroup is isomorphic to. Generators foi the cyclic summands of the torsion subgroups are explicitly computed.

ISSN:0092-7872    

DOI:10.1080/00927879908826542

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826543

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

An element a of a semigroupSis a left magnifier if λa, the inner left translation associated with a, is surjective and is not injective (E. S. Ljapin [11]). When this happens there exists a proper subsetMofSsuch that the restriction toMof λais bijective. In that caseMis said to bea minimal subset for the left magnifier a(F. Migliorini [13], [14], [15]). Remark that ifSis a semigroup having left identities then every left magnifier ofSadmits minimal subsets which are right ideals. Characterisations for semigroups with left magnifiers which also contain left identities have been given by E. S. Ljapin and R. Desq, using the bicyclic monoid. The general problem, precisely to give a characterization of semigroups having left magnifiers, is still open.

ISSN:0092-7872    

DOI:10.1080/00927879908826544

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826509

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor