For a Noetherian local domain (R, m, K), it is an open question whether strong F–regularity deforms. We provide an affirmative answer to this question when the canonical module satisfies certain additional assumptions. The techniques used here involve passing to a Gorenstein ring, using an anti– canonical cover.

A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal oneorthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.

A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal oneorthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.

In this paper, the principal tool to describe transversal polymatroids with Gorenstein base ring is polyhedral geometry, especially the Danilov−Stanley theorem for the characterization of canonical module. Also, we compute the a − invariant and the Hilbert series of base ring associated to this class of transversal polymatroids.

Given a one-dimensional Cohen-Macaulay local ring $$(R,{\mathfrak {m}},k)$$ , we prove that it is almost Gorenstein if and only $${\mathfrak {m}}$$ canonical module of the {m}}:{\mathfrak . Then, generalize this result by introducing notions ideal gAGL proving R an We use fact to characterize when Gorenstein, provided has minimal multiplicity. This generalization proved Chau, Goto, Kumashiro, M...