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In this paper, we give some categorical description of the general spectrum functor, defining it as an adjoint of a global section functor.The general spectrum functor includes that of F1 and of semir...
We give an affirmative answer to the following question by Jarden and Narkiewicz: Is it true that every number field has a finite extension L such that the ring of integers of L is generated by its un...
We study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are particularly simple.
Let F be an affine flat group scheme over a commutative ring R,and S an F-algebra (an R-algebra on which F acts). We define an equivariant analogue QF (S) of the total ring of fractions Q(S) of S.It i...
In this paper we introduce an algebra embedding  : KhXi → S from the free associative algebra KhXi generated by a finite or countable set X into the skew monoid ring S = P ∗  defined by the co...
Let G be a finite graph and K[G] the edge ring of G. Based on the technique of Gr¨obner bases and initial ideals, it will be proved that, given integers f and d with 7  f  d, there exists a finite g...
We study those group rings whose group of units is hyperbolic.Let (X, ) be a metric space with metric . For any a, b, c ∈ X, the Gromov product hb, cia of b and c with respect to a ∈ X is defined as...
Let X be a Mori dream space together with an effective torus action of complexity one. In this note, we construct a polyhedral divisor DCox on a suitable finite covering of P1 which corresponds to the...
We construct via generators and relations, generalized Weil representations for analogues of classical SL(2, k), k a field, over involutive base rings (A, ∗). This family of groups covers diff...
We consider a circle of ideas involving differential algebra, local Noetherian rings, and their generic formal fibers. Connecting these ideas gives rise to what we term a “twisted” subring R of a ring...
We introduce the Andr´e-Quillen cohomology of -rings and -rings, this is different to the -ring cohomology defined by Yau in 2005. We show that there is a natural transformation connecting th...
For an acyclic quiver Q, we solve the Clebsch-Gordan problem for the projective representations by computing the mul-tiplicity of a given indecomposable projective in the tensor product of two indecom...
The main objective of this paper is to give a summary of our recent work on recursion formulae for intersection numbers on moduli spaces of curves and their applications.We also present a conjectural ...
Fuzzy maximal ideals and complete normal fuzzy ideals in G-near-rings are considered, and related properties are investigated.
NASA researchers are presenting a wide range of science results at the 2009 fall meeting of the American Geophysical Union. The meeting opens Dec. 14 and continues through Friday, Dec. 18, at the Mosc...

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