1. bookVolume 29 (2021): Edizione 3 (November 2021)
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eISSN
1844-0835
Prima pubblicazione
17 May 2013
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1 volta all'anno
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access type Accesso libero

On 1-absorbing ╬┤-primary ideals

Pubblicato online: 23 Nov 2021
Volume & Edizione: Volume 29 (2021) - Edizione 3 (November 2021)
Pagine: 135 - 150
Ricevuto: 09 Mar 2021
Accettato: 30 Apr 2021
Dettagli della rivista
License
Formato
Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
Frequenza di pubblicazione
1 volta all'anno
Lingue
Inglese
Abstract

Let R be a commutative ring with nonzero identity. Let ­Łĺą(R) be the set of all ideals of R and let ╬┤ : ­Łĺą (R) Ôćĺ ­Łĺą (R) be a function. Then ╬┤ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J ÔŐć I, we have L ÔŐć ╬┤ (L) and ╬┤ (J) ÔŐć ╬┤ (I). Let ╬┤ be an expansion function of ideals of R. In this paper, we introduce and investigate a new class of ideals that is closely related to the class of ╬┤ -primary ideals. A proper ideal I of R is said to be a 1-absorbing ╬┤ -primary ideal if whenever nonunit elements a, b, c Ôłł R and abc Ôłł I, then ab Ôłł I or c Ôłł ╬┤ (I). Moreover, we give some basic properties of this class of ideals and we study the 1-absorbing ╬┤-primary ideals of the localization of rings, the direct product of rings and the trivial ring extensions.

Keywords

MSC 2010

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