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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 4

Delta operation on modules, prime and radical submodules and primary decomposition

Ashkan Nikseresht
Sayfa
1303–1314
Yayın Tarihi
2022-10-18
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Moreover, we state some conditions under which primary decompositions of submodules of $M$ lift to $M\oplus R$.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let $R$ be a commutative ring with identity and $M$ be an $R$-module.
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Temel Bulgular & Veri:In this paper, in order to study prime submodules, radical submodules and primary decompositions in finitely generated free $R$-modules, we introduce and study an operation $\Delta: (M\oplus R)^2\to M$ defined by $\Delta(m+r, m'+r')= r'm-rm'$.
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Sonuç & Katkı:Moreover, we state some conditions under which primary decompositions of submodules of $M$ lift to $M\oplus R$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Delta operation · primary decomposition · prime submodule

Abstract

Let $R$ be a commutative ring with identity and $M$ be an $R$-module. In this paper, in order to study prime submodules, radical submodules and primary decompositions in finitely generated free $R$-modules, we introduce and study an operation $\Delta: (M\oplus R)^2\to M$ defined by $\Delta(m+r, m'+r')= r'm-rm'$. In particular, using this operation we give a characterization of prime submodules of $M\oplus R$, in terms of prime submodules of $M$. As an application, we present a characterization of prime submodules of finitely generated free modules. Also we present a formula for the prime radical of submodules of $M\dis R$. Moreover, we state some conditions under which primary decompositions of submodules of $M$ lift to $M\oplus R$.

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Bu Makaleye Atıf Yap

Nikseresht, A. (2022). Delta operation on modules, prime and radical submodules and primary decomposition. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 4, 1303–1314. https://ajindex.com/articles/529657

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