… modules X with TX projective over r is representation equivalent to the category of socle-projective
modules … is hereditary, and we describe the Auslander-Reiten quiver of A; in this case ,…

… Since almost all results in [7] about a right peak ring with a homogeneous socle are … socle
projective modules over a right peak ring it and that the relation between the AuslanderReiten …

… \)-modules whose socle is a projective module has almost split sequences. There have been
several papers on which the Auslander–Reiten … projective right \(\varLambda\)-module P, \(\…

… k-algebra with projective socle ( ie socle projective algebra) as left A-module . We consider
the category &(A) of left A-modules with projective socle (ie socle projective modules). One …

… Auslander-Reiten system ending with i. In other words, denoting by « ca representative of a
generator of the socle of … product with UQ lies in the socle of the bimodule which corresponds …

… modules having waists are bounded. Since nonsimple indecomposable injective modules
always have waists, namely their socles… Ifthere exists an indecomposable projective module of …

… entirely of modules with simple socles and tops. Here, n is any finite-dimensional Kalgebra. …
Also, there are only finitely many injective or projective modules, hence 0 must be finite. …

… 19 PI P~ PO p~ M-+ 0 is a minimal projective presentation o9 an indecomposable non-projective
module M • the induced … We inter that the socle o£ AM coincides with the socle of NP …

… that each indecomposable module has a simple socle. Here … simple modules S or b) ~(C) ~
2 for all indecomposable modules … the same number of simple nonprojective modules[14], we …

… (b) We first observe that if P is a projective module, then gP=z P(modA)n9’m(A)~P~ … since
all the simple projective composition factors of a module are in the socle of the module. Let P, …