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This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...

Let A be a hereditary algebra over an algebraically closed field k andA(m) be them-replicated algebra of A. Given an A(m)-module T , we denote by δ(T ) the number of non isomorphic indecomposable summands of T . In this paper, we prove that a partial tilting A(m)module T is a tilting A(m)-module if and only if δ(T ) = δ(A(m)), and that every partial tilting A(m)-module has complements. As an ap...

Let $G$ be a finitely generated abelian group and $M$ be a $G$-graded $A$-module. In general, $G$-associated prime ideals to $M$ may not exist. In this paper, we introduce the concept of $G$-attached prime ideals to $M$ as a generalization of $G$-associated prime ideals which gives a connection between certain $G$-prime ideals and $G$-graded modules over a (not necessarily $G$-graded Noetherian...

The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M , there exists a module K ∈ σ[M ] such that K ⊕N is weakly injective in σ[M ], for any N ∈ σ[M ]. Similarly, if M is projective and right perfect in σ[M ], then there exists a module K ∈ σ[M ] such that K ⊕ N i...

We present the results of a radio polarimetric study of the high-redshift radio galaxy PKS B0529−549 (z = 2.575), based on high-resolution 12 mm and 3 cm images obtained with the Australia Telescope Compact Array (ATCA). The source is found to have a rest-frame Faraday rotation measure of −9600 rad m, the largest seen thus far in the environment of a z > 2 radio galaxy. In addition, the rest-fr...

We present multi-frequency VLBA observations of two polarized Compact Symmetric Objects (CSOs), J0000+4054 and J1826+1831, and a polarized CSO candidate, J1915+6548. Using the wavelength-squared dependence of Fara-day rotation, we obtained rotation measures (RMs) of −180±10 rad m −2 and 1540±7 rad m −2 for the latter two sources. These are lower than what is expected of CSOs (several 1000 rad m...

We evaluated the clinical performance of the Bio-Rad Dx CT/NG/MG assay for the detection of Chlamydia trachomatis, Mycoplasma genitalium and Neisseria gonorrhoeae in urogenital samples in comparison with the Roche COBAS® TaqMan® CT assay for C. trachomatis and an in-house TaqMan PCR assay for M. genitalium. Swab specimens were cultured for N. gonorrhoeae. In this prospective study, urogenital s...

Let M be a module over an associative ring R and σ[M ] the category of M -subgenerated modules. Generalizing the notion of a projective generator in σ[M ], a module P ∈ σ[M ] is called tilting in σ[M ] if (i) P is projective in the category of P -generated modules, (ii) every P -generated module is P presented, and (iii) σ[P ] = σ[M ]. We call P self-tilting if it is tilting in σ[P ]. Examples ...

‎Let $R$ be a domain with quotiont field $K$‎, ‎and‎ ‎let $N$ be a submodule of an $R$-module $M$‎. ‎We say that $N$ is‎ ‎powerful (strongly primary) if $x,yin K$ and‎ ‎$xyMsubseteq N$‎, ‎then $xin R$ or $yin R$ ($xMsubseteq N$‎ ‎or $y^nMsubseteq N$ for some $ngeq1$)‎. ‎We show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $M$‎, ‎also we show tha...