The theory of finitely generated relative (co)tilting modules has been established in the 1980s by Auslander and Solberg, infinitely tilting have recently studied many authors context Gorenstein homological algebra. In this work, we build on developing “Gorenstein approximations” employing these approximations to study classes their associated cotorsion pairs. As applications our results, discu...

We propose a method of generating teaching policies for use in intelligent tutoring systems (ITS) for concept learning tasks [37], e.g., teaching students the meanings of words by showing images that exemplify their meanings à la Rosetta Stone [30] and Duo Lingo [13]. The approach is grounded in control theory and capitalizes on recent work by [28], [29] that frames the “teaching” problem as th...

Let I be an m-primary ideal in a Gorenstein local ring (A,m) with dimA = d, and assume that I contains a parameter ideal Q in A as a reduction. We say that I is a good ideal in A if G = ∑ n≥0 I n/In+1 is a Gorenstein ring with a(G) = 1−d. The associated graded ring G of I is a Gorenstein ring with a(G) = −d if and only if I = Q. Hence good ideals in our sense are good ones next to the parameter...