Let T be a torus and B a compact T−manifold. Goresky, Kottwitz, and MacPherson show in [GKM] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H∗ T (B) as a subring of H∗ T (B ). In this paper we prove an analogue of this result for T−equivariant fiber bundles: we show that if M is a T−manifold and...

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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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.

We describe a theory of logarithmic Chow rings and tautological subrings for logarithmically smooth algebraic stacks, via generalisation the notion piecewise-polynomial functions. Using this machinery we prove that double-double ramification cycle lies in subring (classical) ring moduli space curves, double is divisorial (as conjectured by Molcho, Pandharipande, Schmitt).