A semi-dualizing module over a commutative noetherian ringA is a finitely generated module C with RHomA(C,C) ≃ A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call C–Gorenstein projective, C–Gorenstein injective, and C–Gorenstein flat dimension, and investigate the properties of these dimensions.

The tool used to convert sunlight into electrical energy and increase the temperature of solar cells is called a Solar Panel.To energy, photovoltaic modules are needed. One aspect that effects intensity light. influential aspects conversion light intensity. this directly proportional value energy. greater intensity, produced by panel vice versamore more gets versa. will be optimal when exposed ...

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 OK be a complete discrete valuation ring of residue characteristic p > 0, and G be a finite flat group scheme over OK of order a power of p. We prove in this paper that the Abbes-Saito filtration of G is bounded by a linear function of the degree of G. Assume OK has generic characteristic 0 and the residue field of OK is perfect. Fargues constructed the higher level canonical subgroups for ...

The aim of this paper was to study the applicability of the release module assemblage technology for an adaptable control of drug delivery rate and site. The elementary release module was a swellable matrix having one base convex and the other concave, named Dome Matrix. The swelling and release behavior of the release module was studied. The presence of the convex and concave bases in the swel...

In this paper, we provide a survey (both theoretical and computational) of the conditions for determining which finite p -groups are strongly flat. Let m(G) denote the maximum size of an irredundant generating set of a group G . Then, a group G is strongly flat if m(G) is strictly greater than m(H) for all proper subgroups H of G . For example, J. Whiston has shown in his dissertation that all ...