Communications in Algebra

Alajbegović, Jusuf H.; Osmanagić, Enver

doi: 10.1080/00927879008824008pmid: N/A

González, S.; Martí, C.

doi: 10.1080/00927879008824009pmid: N/A

The aim of this paper is to obtain information about a periodic Jordan ring by using only properties of its idempotent elements. Osborn proves that a power-associative periodic ring having only one nonzero idempotent element is a division ring. so associative. He also proves that a periodic Jordan ring is a subdirect product of simple periodic Jordan rings and that a simple periodic Jordan ring is either a periodic field or a Jordan ring of capacity 2. Using these results we obtain some necessary and suficient conditions for a periodic Jordan ring to be associative, and these conditions are only given in terms of the idempotent elements. We also characterize the periodic Jordan ring which are a direct product of periodic fields and simple periodic Jordan rings of capacity two.

Giuffrida, Salvatore; Maggioni, Renato

doi: 10.1080/00927879008824010pmid: N/A

Conrad, Paul; Martinez, Jorge

doi: 10.1080/00927879008824011pmid: N/A

This article introduces the concept of a very large subgroup in the theory of lattice-ordered groups. The existence of a minimal very large subgroup is connected to some previously known structure theory, but it is also linked to conditions not studied before. Very large subgroups are useful in studying torsion and radical classes, and among other things, extension of lattice-ordered groups using very large kernels yields an intriguing completion operation for torsion classes. In the final section there is a new contruction which produces a lattice-ordered group in which every value is essential, having no special values.

Meierfrankenfeld, U.; Stroth, G.

doi: 10.1080/00927879008824012pmid: N/A

Let G he a finite group and V a faithful, finite dimensional GF 2 G-module. We call E ≤G quadratic,if[V,E,E]=1 and |E|≥4, and we say V is quadratic, if G is generated by its quadratic subgroups. It is an easy exercise, but important for what follows, to show that E has to be elementary abelian. Elementary abelian groups acting quadratically come up quite naturally in weak-closure arguments, pushing-up problems and in problems dealing with parabolic systems. As a successor of [MS] we treat the case that G is a sporadic simple group or an alternating group.

Naudé, Cornelia

doi: 10.1080/00927879008824013pmid: N/A

zafrullah, Muhammad

doi: 10.1080/00927879008824014pmid: N/A

Sladek, Andrzej

doi: 10.1080/00927879008824015pmid: N/A

Portelli, Dario; Spangher, Walter

doi: 10.1080/00927879008824016pmid: N/A

This paper deals with the following problem. Robbiano showed in [9] that standard bases, Gröbner bases, Macaulay bases are all instances of the same general situation. In this paper, we develop this philosophy from the point of view of the Rees algebra R of a ring A w.r.t. a filtration F given on A. The ring R plays a fine job between A and the graded ring G associated to A, F. The use of R and the properties of termorderings and their relate Gröbner bases led naturally to the definition of Gröbnerfiltrations ingeneral commutative rings.

Yun, Fan

doi: 10.1080/00927879008824017pmid: N/A