… a coherent local ring R with finitely generated maximal ideal J and finite weak global dimension…
aim is to extend the Auslander-Buchsbaum Theorem to any commutative coherent rings. …

… method of homological algebra, presented dimensions of formal power series … dimensions
of modules as well as between presented dimensions of rings when R,R[[x]] are coherent rings…

… parallel to the one used to determine the global dimension in classical homological algebra.
… Gorenstein ring. Whereas Ri is a non-noetherian coherent ring and hence is not Gorenstein. …

… [8] and Gorenstein flat modules [10] and developed Gorenstein homological algebra [9]
on modules over a ring R. Various generalizations of these modules are given over specific …

… tain characterizations of Gorenstein n—cotorsion dimension of modules and rings are …
n—cotorsion global dimension of fight凡一coherent rings and other homological dimensions are …

… Homological dimension over coherent semi- local rings Ⅱ [ J]. Pitman Research Notes in
Math … Spectrum and homological dimension of a subring of Q [x ] [ J]. J of N anjing U niv M a th …

… with the Gorenstein homological dimension theory. Some references are [1-2]. Nevertheless,
it is convenient to give a brief history of the Gorenstein homological dimension theory. …

… of modules and rings share many nice properties as the classical homological dimensions.
… that slightly (mꎬn)-coherent rings are von-Neumann regular rings are given. Key words: (mꎬn…

… Gorenstein homological theory plays an important role in relative … Let R be a right
coherent ring, every left R-module has finite Y-Gorenstein flat dimension, and A be a nonempty …

… Abstract: To study homological dimensions, the finiteness of the weak global dimension
of algebras was investigated by the theory of recollements. Assume that (D(Mod B),D(Mod A),D( …