For finitely generated module M over a local ring R, the conventional notions of complete intersection dimension CI-dimRM and CohenMacaulay dimension CM-dimRM do not extend to cover the case of infinitely generated modules. In this paper we introduce similar invariants for not necessarily finitely generated modules, (namely, complete intersection flat and Cohen-Macaulay flat dimensions) which f...

The BMS (Bondi--van der Burg--Metzner--Sachs) symmetry arises as the asymptotic of flat spacetime at null infinity. In particular, algebra for three-dimensional (${\mathrm{BMS}}_{3}$) is generated by super-rotation generators that form a Virasoro subalgebra with central charge ${c}_{L}$, together mutually commuting super-translation generators. and supertranslation have nontrivial commutation r...

We establish equivalent conditions under which every right Rmodule has an epic X -envelope, when X is a Tor-orthogonal class of left-Rmodules. As particular cases, one may recover and complete known results on various generalizations of flatness. MSC 2000. 16D50, 16D40.

In this paper, we principally explore flat modules over a commutative ring with identity. We do this in relation to projective and injective modules with the help of derived functors like Tor and Ext. We also consider an extension of the property of flatness and induce analogies with the “special cases” occurring in flat modules. We obtain some results on flatness in the context of a noetherian...

Let [Formula: see text] be a ring, class of text]-modules and an integer. We introduce the concepts Gorenstein text]-[Formula: text]-injective text]-flat modules via special finitely presented modules. Besides, we obtain some equivalent properties these on text]-coherent rings. Then investigate relations among text]-injective, text]-flat, injective flat text]-rings (i.e., self rings). Several k...

Reverse osmosis is a commonly used process in water desalination. Due to the scarcity of freshwater resources and wastewater problems, a lot of theory and experimental studies have been conducted to optimize this process. In the present study, the performance of reverse osmosis membrane module of salt–water separation was simulated based on computational fluid dynamics technique and solution-di...

For a prime number p > 2, we give a direct proof of Breuil’s classification of finite flat group schemes killed by p over the valuation ring of a p-adic field with perfect residue field. As application we establish a correspondence between finite flat group schemes and Faltings’s strict modules which respects associated Galois modules via the Fontaine-Wintenberger field-of-norms functor

Let Xbe an irreducible algebraic variety defined over a field k. let ¡X be a sheaf of (noncommutative) noetherian A-algebras on X containing the sheaf of regular functions 0 and let R be the ring of global sections. We show that under quite reasonable abstract hypotheses (concerning the existence of a faithfully flat overring of R obtained from the local sections of ifî) there is an equivalence...