Related papers: Multiplicative closure operations on ring extensio…

Given a classical semisimple complex algebraic group G and a symmetric pair (G,K) of Hermitian type, we study the closures of the spherical nilpotent K-orbits in the isotropy representation of K. We show that all such orbit closures are…

Given a right R-module M and any short exact sequence of right R-modules \[ 0 \to A \to B \to C \to 0, \] it is well known that if both A and C belong to the subinjectivity domain $\mathfrak{\underline{In}^{-1}}(M)$ (resp., the…

We investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences w.r.t. the term condition commutator. Then we use the topological structure of the minimal…

Based on a relative Wu theorem in \'etale cohomology, we study the compatibility of Steenrod operations on Chow groups and on \'etale cohomology. Using the resulting obstructions to algebraicity, we construct new examples of non-algebraic…

We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the bounds of cardinalities of definable sets and given sets of…

We define larger variants of the vector spaces one obtains by decategorifying bordered (sutured) Heegaard Floer invariants of surfaces. We also define bimodule structures on these larger spaces that are similar to, but more elaborate than,…

In this note, we prove that a $w$-module $M$ is $w$-Artinian if and only if it is $w$-cofinitely generated and for every prime $w$-ideal $\mathfrak{p}$ of $R$ with $(0:_RM)\subseteq \mathfrak{p}$, there exists a $w$-submodule…

A class of integer-valued functions defined on the set of ideals of an integral domain $R$ is investigated. We show that this class of functions, which we call ideal valuations, are in one-to-one correspondence with countable descending…

We study the injective envelope I(X) of an operator space X, showing amongst other things that it is a self-dual C$^*-$module. We describe the diagonal corners of the injective envelope of the canonical operator system associated with X. We…

We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several…

Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…

Let G be a real, connected, noncompact, semisimple Lie group, let K be a maximal compact subgroup of G, and let g=k+p be the corresponding Cartan decomposition of the complexified Lie algebra of G. Sequences of strongly orthogonal…

If $T$ is a semibounded self-adjoint operator in a Hilbert space $(H, \, (\cdot , \cdot))$ then the closure of the sesquilinear form $(T \cdot , \cdot)$ is a unique Hilbert space completion. In the non-semibounded case a closure is a…

A full subcategory of modules over a commutative ring $R$ is wide if it is abelian and closed under extensions. Hovey \cite{wide} gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms…

We study the ring of differential operators D(X) on the basic affine space X=G/U of a complex semisimple group G with maximal unipotent subgroup U. One of the main results shows that the cohomology group H^*(X,O_X) decomposes as a finite…

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure,…

We define the notion of a partial action on a generalized Boolean algebra and associate to every such system and commutative unital ring $R$ an $R$-algebra. We prove that every strongly $E^{\ast}$-unitary inverse semigroup has an associated…

We define and study binary operations for homotopy groups with coefficients. We give conditions to prove that certain binary operations are the homomorphic image of the generalized Whitehead product. This allows carrying over properties of…

Let G be a compact connected Lie group and H, the centralizer of a one-parameter subgroup in G. Combining the ideas of Bott-Samelson resulotions of Schubert varieties and the enumerative formula on a twisted products of 2-spheres obatained…

Consider the mod 2 homology spectral sequence associated to a cosimplicial space X. We construct external operations whose target is the spectral sequence associated to E\Sigma_2 \times_{\Sigma_2} (X\times X). If X is a cosimplicial…