Related papers: On Modules Whose Pure Submodules Are Essential in …

In this article, we introduce the concepts of graded $s$-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules,…

Tight and essentially tight modules generalize weakly injective modules. Essential tightness requires embeddings to be essential. This restriction makes the two notions totally different. In this note, we investigate cases when those two…

We prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of a cohomological…

We show that for two classes of $m$-secant curves $X \subset S$, with $m \geq 2$, where $f : S = \mathbb{P} (\mathcal{O}_Y \oplus \mathcal{O}_Y (E)) \to Y$ and $E$ is a non-special divisor on a smooth curve $Y$, the Tschirnhausen module…

We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…

In this paper, we extend previous results to prove that generalized modular forms with rational Fourier expansions whose divisors are supported only at the cusps and certain other points in the upper half plane are actually classical…

In a compactly generated triangulated category, we introduce a class of tilting objects satisfying certain purity condition. We call these the decent tilting objects and show that the tilting heart induced by any such object is equivalent…

Let $R$ be a commutative ring with identity and $D$ an $R$-module. It is shown that if $D$ is pure injective, then $D$ is isomorphic to a direct summand of the direct product of a family of finitely embedded modules. As a result, it follows…

In this paper we continue the program on the classification of extensions of the Standard Model of Particle Physics started in arXiv:2007.01660. We propose four complementary questions to be considered when trying to classify any class of…

We study simple and projective modules of a certain class of Ehresmann semigroups, a well-studied generalization of inverse semigroups. Let $S$ be a finite right (left) restriction Ehresmann semigroup whose corresponding Ehresmann category…

The separability tensor element of a separable extension of noncommutative rings is an idempotent when viewed in the correct endomorphism ring; so one speaks of a separability idempotent, as one usually does for separable algebras. It is…

We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence…

We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…

New exact modular branching rules are obtained for modules over the symmetric groups that are close to completely splittable modules. These results are based on some upper bounds for the Ext^1-spaces between simple modules.

The purpose of this paper is to give some new Diophantine applications of modularity results. We use the Shimura-Taniyama conjecture to prove effective finiteness results for integral points on moduli schemes of elliptic curves. For several…

Gromov introduced the notion of a pyramid as a generalization of a metric measure space, based on the idea of the concentration of measure phenomenon. In this paper, we introduce the concept of a direct sum of pyramids, which naturally…

The structure of cyclically pure injective modules over a commutative ring $R$ is investigated and several characterizations for them are presented. In particular, we prove that a module $D$ is cyclically pure injective if and only if $D$…

We study the finite dimensional modules on the half-quantum group u_q^+ at a root of unity q, whose action can be extended to u_q (quotient of the quantized enveloping algebra of sl_2). We derive decomposition formulas of the tensor product…

We develop a theory of separable ring extensions and separable functors for nonunital rings in the setting of firm modules. We prove nonunital analogues of classical results on functorial separability and semisimplicity, and apply these…

A powerful new perspective in the analysis of absolute Galois groups has recently emerged from the study of Galois modules related to classical parameterizing spaces of certain Galois extensions. The recurring trend in these decompositions…