Commun. Korean Math. Soc. 2024; 39(1): 93-104
Online first article January 26, 2024 Printed January 31, 2024
https://doi.org/10.4134/CKMS.c230134
Copyright © The Korean Mathematical Society.
El Mehdi Bouba , Yassine EL-khabchi, Mohammed Tamekkante
Mohammed First University; University Moulay Ismail Meknes; University Moulay Ismail Meknes
Let $R$ be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi $J$-ideals lying properly between the class of $J$-ideals and the class of quasi $J$-ideals. A proper ideal $I$ of $R$ is called a strongly quasi $J$-ideal if, whenever $a$, $b\in R$ and $ab\in I$, then $a^{2}\in I$ or $b\in {\rm Jac}(R)$. Firstly, we investigate some basic properties of strongly quasi $J$-ideals. Hence, we give the necessary and sufficient conditions for a ring $R$ to contain a strongly quasi $J$-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi $J$-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.
Keywords: $J$-ideals, quasi $J$-ideals, strongly quasi $J$-ideals
MSC numbers: Primary 13A15, 13A99
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