Projective modules and orbit space of unimodular rows over Discrete Hodge algebras over a non-Noetherian ring

2018 ◽  
Vol 10 (3) ◽  
pp. 435-455
Author(s):  
Md. Ali Zinna
Keyword(s):  
Noetherian Ring ◽  
Orbit Space ◽  
Projective Modules

Strict Mittag–Leffler modules over Gorenstein injective modules

2019 ◽  
Vol 19 (03) ◽  
pp. 2050050 ◽  
Author(s):  
Yanjiong Yang ◽  
Xiaoguang Yan
Keyword(s):  
Noetherian Ring ◽  
Direct Limit ◽  
Injective Module ◽  
Noetherian Rings ◽  
Projective Modules ◽  
Injective Modules ◽  
Pure Submodules ◽  
Covering Class ◽  
Gorenstein Injective ◽  
Finitely Presented

In this paper, we study the conditions under which a module is a strict Mittag–Leffler module over the class [Formula: see text] of Gorenstein injective modules. To this aim, we introduce the notion of [Formula: see text]-projective modules and prove that over noetherian rings, if a module can be expressed as the direct limit of finitely presented [Formula: see text]-projective modules, then it is a strict Mittag–Leffler module over [Formula: see text]. As applications, we prove that if [Formula: see text] is a two-sided noetherian ring, then [Formula: see text] is a covering class closed under pure submodules if and only if every injective module is strict Mittag–Leffler over [Formula: see text].

scholarly journals Polynomial rings and their projective modules

1989 ◽  
Vol 113 ◽  
pp. 121-128 ◽  
Author(s):  
Dorin Popescu
Keyword(s):  
Noetherian Ring ◽  
Projective Module ◽  
Polynomial Rings ◽  
Projective Modules ◽  
Central Question ◽  
Finitely Generated

Let R be a regular noetherian ring. A central question concerning projective modules over polynomial R-algebras is the following.(1.1) BASS-QUILLEN CONJECTURE ([2] Problem IX, [10]). Every finitely generated projective module P over a polynomial R-algebra R[T], T = (T1,…, Tn) is extended from R, i.e.P≊R[T]⊗R P/(T)P.

scholarly journals Faithfully Exact Functors and Their Applications to Projective Modules and Injective Modules

1964 ◽  
Vol 24 ◽  
pp. 29-42 ◽  
Author(s):  
Takeshi Ishikawa
Keyword(s):  
General Theory ◽  
Noetherian Ring ◽  
Projective Module ◽  
Special Kind ◽  
Projective Modules ◽  
Flat Module ◽  
Commutative Case ◽  
Injective Modules ◽  
Equivalent Conditions

The aim of this paper is to study a property of a special kind of exact functors and give some applications to projective modules and injective modules.In section 1 we introduce the notion of faithfully exact functors [Definition 1] as a generalization of the functor T(X) = X⊗M, where M is a faithfully flat module, and give a property of this class of functors [Theorem 1.1]. Next, applying this general theory to functors ⊗ and Horn, we define the notion of faithfully projective modules [Definition 2] and faithfully injective modules [Definition 3]. In the commutative case “faithfully projective” means, however, simply “projective and faithfully flat” [Proposition 2.3]. In section 2, equivalent conditions for a projective module P to be faithfully projective are given [Theorem 2.2, Proposition 2. 3 and 2.4]. And a simpler proof is given to Y. Hinohara’s result [6] asserting that projective modules over an indecomposable weakly noetherian ring are faithfully flat [Proposition 2.5]. In section 3, we consider faithfully injective modules.

Triangulated Equivalences Involving Gorenstein Projective Modules

2017 ◽  
Vol 60 (4) ◽  
pp. 879-890 ◽  
Author(s):  
Yuefei Zheng ◽  
Zhaoyong Huang
Keyword(s):  
Noetherian Ring ◽  
Derived Category ◽  
Projective Modules ◽  
Injective Dimension ◽  
Stable Category ◽  
Dualizing Complex ◽  
Injective Modules ◽  
Gorenstein Projective Modules ◽  
Left And Right

AbstractFor any ring R, we show that, in the bounded derived category Db(Mod R) of left R-modules, the subcategory of complexes with finite Gorenstein projective (resp. injective) dimension modulo the subcategory of complexes with finite projective (resp. injective) dimension is equivalent to the stable category (resp. ) of Gorenstein projective (resp. injective) modules. As a consequence, we get that if R is a left and right noetherian ring admitting a dualizing complex, then and are equivalent.

Co-absolutely co-pure modules

1986 ◽  
Vol 29 (3) ◽  
pp. 289-298 ◽  
Author(s):  
V. A. Hiremath
Keyword(s):  
Noetherian Ring ◽  
Projective Modules ◽  
Frobenius Ring ◽  
Dedekind Domains ◽  
Flat Modules ◽  
Classical Ring

B. Maddox [15] defined absolutely pure modules and derived some interesting properties of these modules. C. Megibben [17] continued the study of these modules and found more interesting properties. We introduce in this paper co-absolutely co-pure modules as dual to absolutely pure modules. We first prove that over a commutative classical ring these modules are precisely the flat modules. As a biproduct we get a projective characterization of flat modules over a commutative co-noetherian ring. Secondly, over a quasi-Frobenius ring R, co-absolutely co-pure right R-modules turn out to be projective modules. Finally we get a characterization of almost Dedekind domains in terms of co-absolutely co-pure modules.

Quasi-primaryful modules

2015 ◽  
Vol 08 (03) ◽  
pp. 1550051
Author(s):  
Hosein Fazaeli Moghimi ◽  
Mahdi Samiei
Keyword(s):  
Commutative Ring ◽  
Noetherian Ring ◽  
Artinian Ring ◽  
The Other ◽  
Noetherian Rings ◽  
Projective Modules ◽  
New Class ◽  
The Family ◽  
Free Modules ◽  
Finitely Generated Modules

Let [Formula: see text] be a commutative ring with identity. The purpose of this paper is to introduce and to study a new class of modules over [Formula: see text] called quasi-primaryful [Formula: see text]-modules. This class contains the family of finitely generated modules properly, on the other hand it is contained in the family of primeful [Formula: see text]-modules properly, and three concepts coincide if they are multiplication modules. We show that free modules, projective modules over domains and faithful projective modules over Noetherian rings are quasi-primaryful modules. In particular, if [Formula: see text] is an Artinian ring, then all [Formula: see text]-modules are quasi-primaryful and the converse is also true when [Formula: see text] is a Noetherian ring.

Subprojectivity domains of pure-projective modules

2019 ◽  
Vol 19 (05) ◽  
pp. 2050091
Author(s):  
Yılmaz Durğun
Keyword(s):  
Noetherian Ring ◽  
Projective Module ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Projective Modules ◽  
Finitely Generated ◽  
Flat Modules ◽  
Necessary And Sufficient

In a recent paper, Holston et al. have defined a module [Formula: see text] to be [Formula: see text]-subprojective if for every epimorphism [Formula: see text] and homomorphism [Formula: see text], there exists a homomorphism [Formula: see text] such that [Formula: see text]. Clearly, every module is subprojective relative to any projective module. For a module [Formula: see text], the subprojectivity domain of [Formula: see text] is defined to be the collection of all modules [Formula: see text] such that [Formula: see text] is [Formula: see text]-subprojective. We consider, for every pure-projective module [Formula: see text], the subprojective domain of [Formula: see text]. We show that the flat modules are the only ones sharing the distinction of being in every single subprojectivity domain of pure-projective modules. Pure-projective modules whose subprojectivity domain is as small as possible will be called pure-projective indigent (pp-indigent). Properties of subprojectivity domains of pure-projective modules and of pp-indigent modules are studied. For various classes of modules (such as simple, cyclic, finitely generated and singular), necessary and sufficient conditions for the existence of pp-indigent modules of those types are studied. We characterize the structure of a Noetherian ring over which every (simple, cyclic, finitely generated) pure-projective module is projective or pp-indigent. Furthermore, finitely generated pp-indigent modules on commutative Noetherian hereditary rings are characterized.

scholarly journals Max-projective modules

2020 ◽  
pp. 2150095
Author(s):  
Yusuf Alagöz ◽  
Engi̇n Büyükaşık
Keyword(s):  
Noetherian Ring ◽  
Canonical Projection ◽  
Small Ring ◽  
Projective Modules ◽  
Projection Formula ◽  
Commutative Noetherian Ring ◽  
Perfect Ring ◽  
Injective Modules

Weakening the notion of [Formula: see text]-projectivity, a right [Formula: see text]-module [Formula: see text] is called max-projective provided that each homomorphism [Formula: see text], where [Formula: see text] is any maximal right ideal, factors through the canonical projection [Formula: see text]. We study and investigate properties of max-projective modules. Several classes of rings whose injective modules are [Formula: see text]-projective (respectively, max-projective) are characterized. For a commutative Noetherian ring [Formula: see text], we prove that injective modules are [Formula: see text]-projective if and only if [Formula: see text], where [Formula: see text] is [Formula: see text] and [Formula: see text] is a small ring. If [Formula: see text] is right hereditary and right Noetherian then, injective right modules are max-projective if and only if [Formula: see text], where [Formula: see text] is a semisimple Artinian and [Formula: see text] is a right small ring. If [Formula: see text] is right hereditary then, injective right modules are max-projective if and only if each injective simple right module is projective. Over a right perfect ring max-projective modules are projective. We discuss the existence of non-perfect rings whose max-projective right modules are projective.

Invariance of projective modules in $$\mathsf {Sup}$$ under self-duality

2021 ◽  
Vol 82 (1) ◽  
Author(s):  
Javier Gutiérrez García ◽  
Ulrich Höhle ◽  
Tomasz Kubiak
Keyword(s):  
Projective Modules ◽  
Self Duality

Electromagnetic-launch-based method for cost-efficient space debris removal

2020 ◽  
Vol 29 (1) ◽  
pp. 94-106
Author(s):  
Chongyuan Hou ◽  
Yuan Yang ◽  
Yikang Yang ◽  
Kaizhong Yang ◽  
Xiao Zhang ◽  
...  
Keyword(s):  
Space Debris ◽  
Orbit Space ◽  
Low Earth Orbit ◽  
Research Progress ◽  
Area Of Interest ◽  
Electromagnetic Launch ◽  
Debris Removal ◽  
Significant Research ◽  
Electromagnetic Launcher ◽  
Cost Efficient

AbstractThe increase in space debris orbiting Earth is a critical problem for future space missions. Space debris removal has thus become an area of interest, and significant research progress is being made in this field. However, the exorbitant cost of space debris removal missions is a major concern for commercial space companies. We therefore propose the debris removal using electromagnetic launcher (DREL) system, a ground-based electromagnetic launch system (railgun), for space debris removal missions. The DREL system has three components: a ground-based electromagnetic launcher (GEML), suborbital vehicle (SOV), and mass of micrometer-scale dust (MSD) particles. The average cost of removing a piece of low-earth orbit space debris using DREL was found to be approximately USD 160,000. The DREL method is thus shown to be economical; the total cost to remove more than 2,000 pieces of debris in a cluster was only approximately USD 400 million, compared to the millions of dollars required to remove just one or two pieces of debris using a conventional space debris removal mission. By using DREL, the cost of entering space is negligible, thereby enabling countries to remove their space debris in an affordable manner.

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