For n = 2 − 4, m > 2, we determine the cup-length of H∗(G̃n,3;Z/2) by finding a Gröbner basis associated with a certain subring, where G̃n,3 is the oriented Grassmann manifold SO(n + 3)/SO(n)× SO(3). As an application, we provide not only a lower but also an upper bound for the LS-category of G̃n,3. We also study the immersion problem of G̃n,3.

Given two rings R ⊆ S, S is said to be a minimal ring extension of R if R is a maximal subring of S. In this article, we study minimal extensions of an arbitrary ring R, with particular focus on those possessing nonzero ideals that intersect R trivially. We will also classify the minimal ring extensions of prime rings, generalizing results of Dobbs, Dobbs & Shapiro, and Ferrand & Olivier on com...

Let F be a field, let D be a subring of F , and let X be the Zariski-Riemann space of valuation rings containing D and having quotient field F . We consider the Zariski, inverse and patch topologies on X when viewed as a projective limit of projective integral schemes having function field contained in F , and we characterize the locally ringed subspaces of X that are affine schemes.

The moduli space of curves has proven itself a central object in geometry. The past decade has seen substantial progress in understanding the moduli space of curves, involving ideas, for example, from geometry (algebraic, symplectic, and differential), physics, topology, and combinatorics. Many of the new ideas are related to the tautological ring of the moduli space, a subring of the cohomolog...

We characterize ring spectra morphisms from the algebraic cobordism spectrum MGL ([12]) to an oriented spectrum E (in the sense of Morel [4]) via formal group laws on the ”topological” subring E∗ = ⊕iE 2i,i of E∗∗. This result is then used to construct for any prime p a motivic Quillen idempotent on MGL(p). This defines the BP -spectrum associated to the prime p as in Quillen’s [6] for the comp...

If R is an integral domain and K is its field of fractions, we let Int(R) stand for the subring of K[x] which maps R into itself. We show that if R is the ring of integers of a p-adic field, then Int(R) is generated, as an R-algebra, by the coefficients of the endomorphisms of any Lubin-Tate group attached to R.

In answering questions from [7] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V , and let st : V → k be the corresponding standard part map. Under a mild assumption on (R, V) we show that definable sets X ⊆ V n admit a triangulation that induces a triangulation of its standard part st(X) ⊆ k n .

In this paper, we introduce the Harish-Chandra homomorphism for quantum superalgebra $$\mathrm {U}_q({\mathfrak {g}})$$ associated with a simple basic Lie $${\mathfrak {g}}$$ and give an explicit description of its image. We use it to prove that center is isomorphic subring ring $$J({\mathfrak exponential super-invariants in sense Sergeev Veselov, establishing type theorem . As byproduct, obtai...

Given a right ideal I in ring R, the idealizer of R is largest subring which becomes two-sided ideal. In this paper we consider idealizers second Weyl algebra A2, differential operators on k[x,y] (in characteristic 0). Specifically, let f be polynomial x and y defines an irreducible curve whose singularities are all cusps. We show that fA2 A2 always left noetherian, extending work McCaffrey.

A local ring is an associative with unique maximal ideal. We associate each Artinian singleton basis four invariants (positive integers) p,n,s,t. The purpose of this article to describe the structure such rings and classify them (up isomorphism) same invariants. Every can be constructed over its coefficient subring by a certain polynomial called associated polynomial. These polynomials play sig...