ADDENDUM AND CORRIGENDUM TO “WEAK (C11 +) MODULES WITH ACC OR DCC ON ESSENTIAL SUBMODULES”

Source abstract

It has come to our attention that there is a positive answer to the following question mentioned in [2, p. 734] : ``We may conjecture whether a $(WC_{11})$-module with essential socle is a $(C_{11})$-module? ". Unfortunately in [2, Example 9] we mistakenly stated that \begin{eqnarray*} R=\Big[\begin{array}{ll} \mathbb{Z}/\mathbb{Z}p^{2} & \mathbb{Z}/\mathbb{Z}p^{2} \\ 0 & \mathbb{Z}/\mathbb{Z}p^{2} \end{array}\Big] \end{eqnarray*} is not right $(C_{11})$. However this $R$ is, in fact, right $(C_{11})$ (see, [1, Theorem 2.4]). Moreover the following proposition provides the answer to the question which do not affect the other results in the paper.