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

#### Ashkan NİKSERESHT [1]

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 $M\oplus R$.
Delta operation, primary decomposition, prime submodule, radical of submodules
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-4422-8782Author: Ashkan NİKSERESHT (Primary Author)Institution: Shiraz UniversityCountry: Iran Publication Date : August 6, 2020
 Bibtex @research article { hujms667410, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1303 - 1314}, doi = {10.15672/hujms.667410}, title = {Delta operation on modules, prime and radical submodules and primary decomposition}, key = {cite}, author = {Ni̇kseresht, Ashkan} } APA Ni̇kseresht, A . (2020). Delta operation on modules, prime and radical submodules and primary decomposition . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1303-1314 . DOI: 10.15672/hujms.667410 MLA Ni̇kseresht, A . "Delta operation on modules, prime and radical submodules and primary decomposition" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1303-1314 Chicago Ni̇kseresht, A . "Delta operation on modules, prime and radical submodules and primary decomposition". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1303-1314 RIS TY - JOUR T1 - Delta operation on modules, prime and radical submodules and primary decomposition AU - Ashkan Ni̇kseresht Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.667410 DO - 10.15672/hujms.667410 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1303 EP - 1314 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.667410 UR - https://doi.org/10.15672/hujms.667410 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Delta operation on modules, prime and radical submodules and primary decomposition %A Ashkan Ni̇kseresht %T Delta operation on modules, prime and radical submodules and primary decomposition %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.667410 %U 10.15672/hujms.667410 ISNAD Ni̇kseresht, Ashkan . "Delta operation on modules, prime and radical submodules and primary decomposition". Hacettepe Journal of Mathematics and Statistics 49 / 4 (August 2020): 1303-1314 . https://doi.org/10.15672/hujms.667410 AMA Ni̇kseresht A . Delta operation on modules, prime and radical submodules and primary decomposition. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1303-1314. Vancouver Ni̇kseresht A . Delta operation on modules, prime and radical submodules and primary decomposition. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1303-1314.

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