Loewy length of modules over almost perfect domains

Abstract

A construction of local almost perfect domains R-n such that the Loewy length of Q(n)/R-n is omega (n + 1) is performed, where Q(n) is the field of quotients of R-n and n is an arbitrary positive integer. (C) 2004 Elsevier Inc. All rights reserved

On socle chains of semiartinian rings with primitive factors artinian

“…Basic structural results about general semiartinian rings are published in papers [6,7,9,13,15] while papers [3,4,7,14,8] describes properties and constructions of semiartinan rings close to von Neumann regular ones. Recent papers [1,2] are focused to correspondence between the class of semiartinian rings and other interesting classes of rings defined by some property of module categories.…”

Tilting modules over almost perfect domains

“…Although local APD's were studied earlier by R. Smith [48] under the name "local domains with topologically T -nilpotent radical " (local TTN-domains), the interest in them resurfaced only recently in connection with the revival of theory of cotorsion pairs introduced by L. Salce [42]. Our main reference on APD's and their modules is the survey by L. Salce [47] (see also [13], [57], [14], [50], [44], [46], [58], [26]).…”

The class semigroup of local one-dimensional domains

“…Almost perfect domains form a large and interesting class of rings, containing one-dimensional Noetherian domains. The papers [9,33,28,26,27] have been dedicated to the study of local almost perfect domains and their modules.…”