for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

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We establish a formula for the classes of certain tori in the Grothendieck ring of varieties, expressing them in terms of the natural lambda-structure on the Grothendieck ring. More explicitly, we will see that if L∗ is the torus of invertible elements in the n-dimensional separable k-algebra L, then the class of L∗ can be expressed as an alternating sum of the images of the spectrum of L under...

Let k be a subring of the field of rational functions in x, v, s which contains x, v, s. If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations: (1) xL+ − xL− = (s − s)L0; (2) L with a positive twist = (xv)L; (3) L ⊔ O = ( v−v −1 s−s−1 )...

Let R be a number field or a recursive subring of a number field and consider the polynomial ring R[T ]. We show that the set of polynomials with integer coefficients is diophantine over R[T ]. Applying a result by Denef, this implies that every recursively enumerable subset of R[T ]k is diophantine over R[T ].

Construction of the diagrammatic version of the affine Temperley-Lieb algebra of type A N as a subring of matrices over the Laurent polynomials is given. We move towards geometrical understanding of cellular structure of the Temperley-Lieb algebra. We represent its center as a coordinate ring of the certain affine algebraic variety and describe this variety constructing its desingularization.

Let k0 be a field of characteristic not two, (V, b) finite-dimensional regular bilinear space over k0, and W subgroup the orthogonal group with property that subring W-invariants symmetric algebra V is polynomial k0. We prove Serre’s splitting principle holds for cohomological invariants values in Rost’s cycle modules.