In this paper, we prove that the global Gorenstein projective dimension of a ring R is equal to the global Gorenstein injective dimension of R, and that the global Gorenstein flat dimension of R is smaller than the common value of the terms of this equality.

We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular we derive that in any local ring R of mixed...

In this paper, we first present the complete list of the singularity types of the Picard number one Gorenstein log del Pezzo surface and the number of the isomorphism classes with the given singularity type. Then we give out a method to find out all singularity types of Gorenstein log del Pezzo surface. As an application, we present the complete list of the Dynkin type of the Picard number two ...

background: several studies have established that all nurses need continuing education, especially those who are working in oncology wards. in the current programs, there are just two general patterns for teaching: teacher-centered and student-centered patterns. in this study, the effect of teacher-centered (lecture) and student-centered (module) teaching methods in relation to safety standards...

We discuss invariants of Cohen-Macaulay local rings that admit a canonical module $\omega$. Attached to each such ring R, when $\omega$ is an ideal, there are integers--the type the reduction number $\omega$--that provide valuable metrics express deviation R from being Gorenstein ring. In arXiv:1701.05592 and arXiv:1711.09480 we enlarged this list with degree bi-canonical degree. work extend wh...

Q-Gorenstein toric contact manifolds provide an interesting class of examples with torsion first Chern class. They are completely determined by certain rational convex polytopes, called diagrams, and arise both as links isolated singularities prequantizations monotone symplectic orbifolds. In this paper we show how the cylindrical homology invariants a manifold related to Ehrhart (quasi-)polyno...

A ring R is called left GF-closed, if the class of all Gorenstein flat left Rmodules is closed under extensions. The class of left GF-closed rings includes strictly the one of right coherent rings and the one of rings of finite weak dimension. In this paper, we investigate the Gorenstein flat dimension over left GF-closed rings. Namely, we generalize the fact that the class of all Gorenstein fl...

The category gp ( Λ ) of Gorenstein-projective modules over tensor algebra = A ⊗ k B can be described as the monomorphism mon , . In particular, Λ-modules are monic. this paper, we find similar relation between semi-Gorenstein-projective and -modules, via monic modules, namely, ⊥ ∩ Using this, it is proved that if weakly Gorenstein, then Gorenstein only each monic; Q with a finite acyclic quive...

Let Λ and Γ be artin algebras and ΛUΓ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of k-Gorenstein modules with respect to ΛUΓ and then establish the left-right symmetry of the notion of k-Gorenstein modules, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. ...