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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Pure and Applied Algebra
( Vol. 90 NO.1 / (1993))
Posets of Finite Prinjective Type and a Class of Orders
Daniel Simson,
Pages. 77-103
Abstract The main aim of this paper is to give a characterisation of finite
posets $J$ having only finitely many isomorphism classes of
indecomposable socle projective $K$-linear representations over a
given field $K$, or equivalently, finite posets $J$ having only
finitely many indecomposable canonical forms of partitioned
matrices of the shape (2.12) (with coefficients in $K$) with
respect to the $J$-elementary transformations (E$_1$) and (E$_2$)
defined in Section 2. The characterisation is given in Theorem 3.1
in terms of the Tits quadratic form associated to $J$, in terms of
a class of algebraic varieties with an algebraic group action, and
by presenting a critical list of 114 minimal posets having
infinitely many isomorphism classes of indecomposable socle
projective representations An application of posets of finite
prinjective type to the study of indecomposable lattices over a
class of orders is given.
Contents 1. Introduction
2. Prinjective modules and a corresponding matrix problem
3. Posets of finite prinjective type
4. Stratification subproducts of tiled (0,1)-orders
5. Minimal posets $mathcal{P}_1,...,mathcal{P}_{110}$ of infinite prinjective type
Key words
Mathmatical Subject Classification