On the saturations of submodules

Lokendra Paudel; Simplice Tchamna

Geodesic

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On the saturations of submodules

Lokendra Paudel ; Simplice Tchamna

Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 110-123.

Voir la notice de l'article provenant de la source Math-Net.Ru

Résumé

Let

R \subseteq S

be a ring extension, and let

A

be an

R

-submodule of

S

. The saturation of

A

(in

S

) by

τ

is set

A_{[τ]} = {x \in S : A for some t \in τ}

, where

τ

is a multiplicative subset of

R

. We study properties of saturations of

R

-submodules of

S

. We use this notion of saturation to characterize star operations

⋆

on ring extensions

R \subseteq S

satisfying the relation

(A \cap B)^{⋆} = A^{⋆} \cap B^{⋆}

whenever

A

and

B

are two

R

-submodules of

S

such that

A S = B S = S

Keywords: star operation, ring extension, prime spectrum, localization, flat module.
Mots-clés : saturation

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Lokendra Paudel; Simplice Tchamna. On the saturations of submodules. Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 110-123. https://geodesic-test.mathdoc.fr/item/ADM_2018_26_1_a10/

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