“Prime and Radical Submodules of Modules over Commutative Rings” by Marion E. Moore and Sally J. Smith, Comm. Algebra, Volume 30, Issue 10, pp. 5037–5064
Editorial errors occurred to the superscripts in the article, due in no part to the authors. We bring attention to these errors and provide the corrections.
p. 5038 1.1 …If B is maximal, prime, or primary, it is easily shown (as in [1])
p. 5038 1.1 …For details of this fact, see Theorem 1.9 and Example 1.11 of [2]
p. 5038 Lemma 1.1. …Lemma 1.2 is a slight generalization of [1] Theorem 5.8
p. 5039 Theorem 1.3, Proof. …By [1] Theorem 5.6
p. 5039 Theorem 1.5, Proof. …By, [1] each
p. 5039 Theorem 1.5, Proof. …is a prime submodule by [1] Theorem 5.6
p. 5040 Theorem 1.5, Proof. …By [4] Theorem 4.4
p. 5040 Lemma 1.9, Proof. …Moreover, by [4] Theorem 4.4
p. 5041 Lemma 1.9, Proof. …treated for an example in [6]
p. 5042 Corollary 1.13, Proof. …then by [4] Theorem 4.4
p. 5045 Theorem 2.7, Proof. …By, [4] there exists a prime submodule P
p. 5045 Theorem 2.8, Proof. …by [4] Theorem 4.4
p. 5045 Theorem 2.9, Proof. Using [4] Theorem 4.4
p. 5046 3.1 …Much of the theory found in [6]
p. 5047 Example 3.2, Solution. …The next two theorems appear in [6]
p. 5047 Example 3.2, Solution. …are exactly analogous to the proofs given in [6]
p. 5048 Theorem 3.6, Proof. …Using [6] Theorem 4.2.13
p. 5049 Theorem 3.7, Proof. …Every submodule is contained in a maximal submodule which is prime. [1]
p. 5050 Theorem 3.9, Proof. …By [4] Theorem 3.3
p. 5051 Theorem 3.11, Proof. …and so by Corollary 1.13
p. 5052 Theorem 4.1, Proof. …By [4] there exists
p. 5052 Corollary 4.2, Proof. …By Theorem 4.1 and [9] Lemma 1.1
p. 5054 Theorem 4.11, Proof. …for each i and so by, [1]
p. 5055 Theorem 4.13, Proof. …then by [4] Theorem 3.3
p. 5055 Example 4.14 …A(p) is studied in [9]
p. 5055 Example 4.14 …but are not mentioned in [9]
p. 5056 Theorem 4.19, Proof. …By [9] Corollary 1.2
p. 5057 Theorem 4.20, Proof. …By [9] Theorem 1.9
p. 5057 Theorem 4.20, Proof. …The result now follows from [9] Lemma 1.5
p. 5060 Theorem 5.7, Proof. …and so by [4] Theorem 1.5
p. 5063 Example 5.12, Solution. …used in Example 5.12 is not a zero-dimensional ideal