Correction and addendum to: “On algebras of finite representation type”

Abstract

In this note we retain the notation and terminology of our original paper [2]. Our purpose is to repair the statement and proof of Theorem 2.3 of [2], and using its generalization (Theorem A below) as a prototype, we can by use of an extension of Corollary 3.3 of [2] (Theorem B below) remove the weighty hypothesis of from Theorems 3.4, 3.5, 3.6 and Corollary 3.7 of [2]. This latter task derives some urgency from the conjecture of J. P. Jans [3] that an algebra with large kernels has finite module type. This conjecture, if true, would of course annihilate any importance of the above-mentioned results of [2] in its original form as far as the Brauer-Thrall conjecture is concerned(1). CORRECTION 1. The statement of Theorem 2.3 of [2] should read as follows: