Let $Lambda$ be an artin algebra. In his Philadelphia Notes, M. Auslander showed that any homomorphism between $Lambda$-modules is right determined by a $Lambda$-module $C$, but a formula for $C$ which he wrote down has to be modified. The paper presents corresponding counter-examples, but also provides a quite short proof of Auslander’s assertion that any homomorphism is right determined by a module. Using the same methods, we describe the minimal right determiner of a morphism, as discussed in the book by Auslander, Reiten and Smal?. In addition, we look at the role of indecomposable projective direct summands of a minimal right determiner and provide a detailed analysis of the kernel-determined morphisms: these are those morphisms which are right determined by a module without any non-zero projective direct summand. In this way, we answer a question raised in the book by Auslander, Reiten and Smal?. What we encounter is an intimate relationship to the vanishing of $operatorname{Ext}^{2}$.
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机译：令$ Lambda $为artin代数。 M. Auslander在他的费城笔记中指出，$ Lambda $-模块之间的任何同态性都是由$ Lambda $-模块$ C $确定的，但是他写下的$ C $的公式必须修改。该论文提出了相应的反例，但也提供了一个简短的证据证明澳大利亚人的主张，即任何同态都是由模块确定的。正如Auslander，Reiten和Smal？在书中所讨论的，使用相同的方法，我们描述了态射的最小右确定子。此外，我们研究了最小权利确定者的不可分解的射影直接求和的作用，并详细分析了由内核确定的态素：这些是由模块正确确定的射态，没有任何非零的射影直接求和。通过这种方式，我们回答了Auslander，Reiten和Smal？在书中提出的问题。我们遇到的是与 operatorname {Ext} ^ {2} $消失的密切关系。
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