Related papers: Bass modules and embeddings into free modules

We construct embeddings G of the category of graphs into categories of R-modules over a commutative ring R which are almost full in the sense that the maps induced by the functoriality of G R[Hom_Graphs(X,Y)] --> Hom_R(GX,GY) are…

Answering some of the main questions from [MR13], we show that whenever $\kappa$ is a cardinal satisfying $\kappa^{< \kappa} = \kappa > \omega$, then the embeddability relation between $\kappa$-sized structures is strongly invariantly…

Let $A$ be a ring and $R$ be a polynomial or a power series ring over $A$. When $A$ has dimension zero, we show that the Bass numbers and the associated primes of the local cohomology modules over $R$ are finite. Moreover, if $A$ has…

A stationary subset $S$ of a regular uncountable cardinal $\kappa$ {\it reflects fully} at regular cardinals if for every stationary set $T \subseteq \kappa$ of higher order consisting of regular cardinals there exists an $\alpha \in T$…

We study projective presentations of finite-dimensional modules over finite-dimensional algebras. We discuss if projective presentations of maximal rank behave additively. More precisely, we ask if the direct sum of copies of a projective…

We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…

In this note, we are working within the category $\rmod$ of (unitary, left) $R$-modules, where $R$ is a {\bf countable} ring. It is well known (see e.g. Kie{\l}pi\'nski & Simson [5], Theorem 2.2) that the latter condition implies that the…

In this article, we study the notion of a finite $\Sigma$-Rickart module, as a module theoretic analogue of a right semi-hereditary ring. A module $M$ is called \emph{finite $\Sigma$-Rickart} if every finite direct sum of copies of $M$ is a…

Our results in this paper increase the model-theoretic precision of a widely used method for building ultrafilters, and so advance the general problem of constructing ultrafilters whose ultrapowers have a precise degree of saturation. We…

Let $R$ be a commutative Noetherian Henselian local ring. Denote by $\mathrm{mod} R$ the category of finitely generated $R$-modules, and by ${\mathcal G}$ the full subcategory of $\mathrm{mod} R$ consisting of all G-projective $R$-modules.…

We call a right module $M$ (strongly) virtually regular if every (finitely generated) cyclic submodule is isomorphic to a direct summand. $M$ is said to be completely virtually regular if every submodule is virtually regular. In this paper,…

We generalize the theory of logarithmic derivations through a self-contained study of modules here dubbed tangential idealizers. We establish reflexiveness criteria for such modules, provided the ring is a factorial domain. As a main…

If $S,T$ are stationary subsets of a regular uncountable cardinal $\kappa$, we say that $S$ reflects fully in $T$, $S<T$, if for almost all $\alpha \in T$ (except a nonstationary set) $S \cap \alpha$ is stationary in $\alpha .$ This…

It follows from a recent paper by Ding and Wang that any ring which is generalized supplemented as left module over itself is semiperfect. The purpose of this note is to show that Ding and Wang's claim is not true and that the class of…

We show that counterexamples of Iyengar and Walker to the algebraic version of Gunnar Carlsson's conjecture on the rank of the homology of a free complex can be extended to examples over any finite group with many choices of the complex.

Let $R$ be a noetherian commutative ring, and \[ \mathbb F: ...\rightarrow F_2\rightarrow F_1\rightarrow F_0\rightarrow 0 \] a complex of flat $R$-modules. We prove that if $\kappa(\mathfrak p)\otimes_R\mathbb F$ is acyclic for every…

We study Structural Reflection beyond Vop\v{e}nka's Principle, at the level of almost-huge cardinals and higher, up to rank-into-rank embeddings. We identify and classify new large cardinal notions in that region that correspond to some…

We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, $\mathcal{PGF}$, (respectively that of projectively coresolved Gorenstein $\mathcal{B}$ flat modules,…

In this paper, first we obtain some new and interesting results on projective modules and on the upper topology of an ordinal number. Then it is shown that the rank map of a locally of finite type projective module is continuous with…

Let $\Lambda$ be a $\mathbb{Z}$-graded artin algebra. Two classical results of Gordon and Green state that if $\Lambda$ has only finitely many indecomposable gradable modules, up to isomorphism, then $\Lambda$ has finite representation…