论几乎无处不在的 K 正集值映射

IF 0.4 Q4 MATHEMATICS

Annales Mathematicae Silesianae Pub Date : 2023-12-13 DOI:10.2478/amsil-2023-0025

Eliza Jabłońska

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引用次数: 0

摘要

摘要假设 X 是一个阿贝尔群，Y 是一个交换单元，K ⊂Y 是一个子单元，F : X → 2Y \ {∅} 是一个集合值映射。在对 X 中的ℐ1 理想和 X2 中的ℐ2 理想的一些额外假设下，我们证明如果 F 是ℐ2-几乎无处不在的 K-additive 的，那么存在一个唯一的直到 K-additive 的带集合值的映射 G : X → 2Y \{∅} ，使得 F = G ℐ1- 几乎无处不在 X 中。

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On Almost Everywhere K-Additive Set-Valued Maps

Abstract Let X be an Abelian group, Y be a commutative monoid, K ⊂Y be a submonoid and F : X → 2Y \ {∅} be a set-valued map. Under some additional assumptions on ideals ℐ1 in X and ℐ2 in X2, we prove that if F is ℐ2-almost everywhere K-additive, then there exists a unique up to K K-additive set-valued map G : X → 2Y \{∅} such that F = G ℐ1-almost everywhere in X. Our considerations refers to the well known de Bruijn’s result [1].

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来源期刊

Annales Mathematicae Silesianae Mathematics-Mathematics (all)

CiteScore

0.60

自引率

25.00%

发文量

审稿时长

27 weeks