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- W4296709743 abstract "Let [Formula: see text] be a commutative ring with nonzero identity. In this paper, we introduce and investigate a new class of ideals that is closely related to the class of [Formula: see text]-ideals. A proper ideal [Formula: see text] of [Formula: see text] is said to be a [Formula: see text]-ideal if whenever nonunit elements [Formula: see text] and [Formula: see text], then [Formula: see text] or [Formula: see text] Some basic properties of [Formula: see text]-ideals are studied. For instance, we give a method to construct [Formula: see text]-ideals that are not [Formula: see text]-ideals. Among other things, it is shown that if [Formula: see text] admits a [Formula: see text]-ideal that is not an [Formula: see text]-ideal, then [Formula: see text] is a local ring. Also, we provide a necessary and sufficient condition in term of [Formula: see text]-ideals for a ring to be a total quotient ring and we determinate the [Formula: see text]-ideals of a chained ring. Finally, we give an idea about some [Formula: see text]-ideals of the localization of rings, the trivial ring extensions and the power series rings to construct nontrivial and original examples of [Formula: see text]-ideals." @default.
- W4296709743 created "2022-09-23" @default.
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- W4296709743 date "2022-10-28" @default.
- W4296709743 modified "2023-09-26" @default.
- W4296709743 title "On (1,r)-ideals of commutative rings" @default.
- W4296709743 doi "https://doi.org/10.1142/s0219498824500233" @default.
- W4296709743 hasPublicationYear "2022" @default.
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