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**1 - 3**of**3**### t-Prüfer Modules

"... Abstract. In this article, we characterize t-Prüfer modules in the class of faithful multi-plication modules. As a corollary, we also characterize Krull modules. Several properties of a t-invertible submodule of a faithful multiplication module are given. 1. ..."

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Abstract. In this article, we characterize t-Prüfer modules in the class of faithful multi-plication modules. As a corollary, we also characterize Krull modules. Several properties of a t-invertible submodule of a faithful multiplication module are given. 1.

### INTEGRALLY CLOSED MODULES

"... Abstract. In this paper, we find some properties on integrally closed modules. 1. ..."

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Abstract. In this paper, we find some properties on integrally closed modules. 1.

### ON SUBMODULE TRANSFORMS T(N) AND S(N)

"... Abstract. In this paper, we give some properties on submodule transforms. Let M be a module over commutative ring R with identity, S the set of nonzero divisors of R and RS the total quotient ring of R. For a nonzero ideal I of R, let I−1 = {x ∈ RS |xI ⊆ R}. I is said to be an invertible ideal of R ..."

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Abstract. In this paper, we give some properties on submodule transforms. Let M be a module over commutative ring R with identity, S the set of nonzero divisors of R and RS the total quotient ring of R. For a nonzero ideal I of R, let I−1 = {x ∈ RS |xI ⊆ R}. I is said to be an invertible ideal of R if II−1 = R. Put T = {t ∈ S|tm = 0 for some m ∈