Torsion-Free Modules over Reduced Witt Rings

Characterizing Reduced Witt Rings Ii

1-torsion of Finite Modules over Semiperfect Rings

We initiate the study of 1-torsion of finite modules over two-sided noetherian semiperfect rings. In particular, we give a criterion for determining when the 1-torsion submodule contains minimal generators of the module. We also provide an explicit construction for a projective cover of the submodule generated by the torsion elements in the top of the module. Some of the obtained results hold w...

Isotropy and Factorization in Reduced Witt Rings

We consider reduced Witt rings of finite chain length. We show there is a bound, in terms of the chain length and maximal signature, on the dimension of anisotropic, totally indefinite forms. From this we get the ascending chain condition on principal ideals and hence factorization of forms into products of irreducible forms. 2000 Mathematics Subject Classification: 11E81, 12D15

-torsion free Acts Over Monoids

In this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. Then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right Rees factor, cyclic and acts in general  implies some other properties, respectively.

Characterizing Reduced Witt Rings of Fields

Let IV(F) denote the Mitt ring of nondegenerate symmetric bilinear forms over a field F. In this paper wc shall be concerned only with formally real fields, for which we write Wr,,l(F) ~mm W(F)/Wil W(F) for the reduced R’itt ring. In [13, 141 the rings W(F) and iTred are shown to be special cases of absfrart lWtt rirqs and a great deal of the ring structure is developed in this setting. In [6] ...