TY - JOUR
AU - Xi, Changchang
AB - CHANGCHANG XI 1. Introduction Let k be an algebraically closed field and A a finite-dimensional fc-algebra. As usual we assume that A is basic and connected. Thus A is a factor-algebra of the path algebra of a quiver A = (A , A ) by an admissible ideal /. By ,4-mod we denote the o x category of all finitely generated left y4-modules and by A-ind a full subcategory of ,4-mod consisting of the representatives of isomorphism classes of all indecomposable modules. Let xe A ; we denote by P(x), Q(x) and E(x) the indecomposable projective v4-module, the indecomposable injective module and the simple module at the vertex x, respectively. Now we consider the set S£ = {MeA-ind\M £ P(x),Horn(P(x),M) * 0 and Horn(P(x),xM) = 0}, where x stands for the Auslander-Reiten translation, and we define on S the relation X ^ Y if and only if there is a homomorphism/: 7-> X such that Horn (P(x),f) # 0. Let T denote the Auslander-Reiten quiver of A. Thus the vertices of F are A A isomorphism classes [X] of ^-modules Zi n y4-ind. One defines a function h : (T ) -> N x A 0 by h ([X]) 
TI - Minimal Elements of the Poset of a Hammock
JO - Journal of the London Mathematical Society
DO - 10.1112/jlms/s2-46.2.228
DA - 1992-10-01
UR - https://www.deepdyve.com/lp/wiley/minimal-elements-of-the-poset-of-a-hammock-gNEWNU0JyU
SP - 228
EP - 238
VL - s2-46
IS - 2
DP - DeepDyve
ER -