“Prime Modules and Submodules” by Yücel Tiras¸ and Mustafa Alkan, Comm. Algebra®, 31(11), 2003, pp. 5253–5261.
p. 5254 The sentence “if N is any submodule….” has to be corrected as follows:
If N is any submodule of M, following (Naoum, 1996), we say that…
p. 5255 Theorem 2.2 has to be corrected as follows:
Theorem 2.2 (Tιras et al., 2000….)
Any dense submodules of a finitely generated multiplication R-module is also a finitely generated multiplication R-module.
p. 5256 In the proof of Theorem 2.2
The sentence “clearly Clearly | |||||
The sentence “Thus Thus by Tιras et al. (2000), | |||||
The sentence “Since any finitely generated dense submodule….” has to be corected as follows: Since any finitely generated dense submodule of a multiplication R-module is also a multiplication module (see for example, Tιras et al., 2000), N is a multiplication module. |
p. 5258 The sentence “if R is a Dedekind domain (see Jenkins and Smith, 1992; Sharif and Sharif, preprint)” has to be corrected as follows:
If R is a Dedekind domain (see Jenkins and Smith, 1992; Sharif et al., 1996).
p. 5259 The sentence “Now we say that….” has to be corrected as follows:
Now, following (Smith, 2001), we say that…
The sentence “Since the following lemma is…” has to be corrected as follows:
Since the following lemma is known and clear we omit the proof.
p. 5261 The reference “Sharif, H., Sharifi, Y., On a conjecture of Jenkins and Smith, Preprint” has to be corrected as follows:
Sharif, H., Sharifi, Y., Namazi, S. (1996). Rings satisfying the radical formula. Acta. Math. Hungar 71(1–2):103–108.