Related papers: Weak dimension of FP-injective modules over chain …

We obtain bounds on the cardinality of $pcf(\mathfrak{a})$ from instances of weak diamond. Consequently, under mild assumptions there are many singular cardinals of the from $\aleph_\delta$ for which…

A subset $A$ of $\mathbb{Z}^n$ is called a weak antichain if it does not contain two elements $x$ and $y$ satisfying $x_i<y_i$ for all $i$. Engel, Mitsis, Pelekis and Reiher showed that for any weak antichain $A$, the sum of the sizes of…

The aim of this paper is to describe the classes of strongly flat and weakly cotorsion modules with respect to a multiplicative subset or a finite collection of multiplicative subsets in a commutative ring. The strongly flat modules are…

Let $R$ be a regular local ring containing a field $k$ of characteristic $p$ and $M$ be an $\mathscr{F}$-finite module. In this paper, we study the injective dimension of $M$. We prove that $\operatorname{dim}_R(M) -1…

We prove the consistency of the failure of the weak diamond $\Phi_\lambda$ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond $\Psi_\lambda$ is equivalent to the statement $2^{<\lambda}<2^\lambda$ and…

Let $R$ be a commutative ring with a non-zero identity, $S$ be a multiplicatively closed subset of $R$ and $M$ be a unital $R$-module. In this paper, we define a submodule $N$ of $M$ with $(N:_{R}M)\cap S=\phi$ to be weakly $S$-prime if…

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein global dimension and we study the weak Gorenstein homological…

Using the notion of cyclically pure injective modules, a characterization for rings which are locally valuation is established. As applications, new characterizations for Prufer domains and pure semi-simple rings are provided. Namely, we…

It has recently been shown that a minimal reversible nonsymmetric ring has order 256 answering a questioned original posed in a paper on a taxonomy of 2-primal rings. Answers to similar questions on minimal rings relating to this taxonomy…

A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. In the present paper we introduced a weak metric, called the Apollonian weak metric, on any subset of a Euclidean…

This article gives the structure of all projective indecomposable modules in blocks with non-cyclic defect group for $n\leq 11$, and almost all in the case of $n=12$, leaving four simple modules for $p=2$ and one simple module for $p=3$.

This paper introduces a class of Hermitian LCD $2$-quasi-abelian codes over finite fields and presents a comprehensive enumeration of these codes in which relative minimum weights are small. We show that such codes are asymptotically good…

We prove that, for any $n \geq 2$, the classes of $\rm{FP}_{n}$-injective modules and of $\rm{FP}_n$-flat modules are both covering and preenveloping over any ring $R$. This includes the case of $\rm{FP}_{\infty}$-injective and…

In this paper, we investigate the weak Gorenstein global dimensions. We are mainly interested in studying the problem when the left and right weak Gorenstein global dimensions coincide. We first show, for GF-closed rings, that the left and…

Weak ferromagnetism of quasi-one-dimensional S = 1/2 antiferromagnet BaCu$_2$Ge$_2$O$_7$ is studied by the magnetization measurement. The spontaneous magnetization appears along the b axis. The local symmetry between the in-chain nearest…

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring $R$, the ring itself and its canonical module are always realized as (trivial) semidualizing modules. Reasonably, one might…

Let R be a commutative ring with identity and M be an R-module. In this paper, we will introduce the concept of 2-irreducible (resp., strongly 2- irreducible) submodules of M as a generalization of irreducible (resp., strongly irreducible)…

We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a…

Let $R\subset A$ be a Frobenius extension of rings. We prove that: (1) for any left $A$-module $M$, $_{A}M$ is Gorenstein projective (injective) if and only if the underlying left $R$-module $_{R}M$ is Gorenstein projective (injective). (2)…

Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination result for certain modules over finite simple extensions of the…