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- W4287757367 abstract "In this study, we present the generalization of the concept of $r$-ideals in commutative rings with nonzero identity. Let $R$ be a commutative ring with $0neq1$ and $L(R)$ be the lattice of all ideals of $R$. Suppose that $phi:L(R)rightarrow L(R)cupleft{emptysetright}$ is a function. A proper ideal $I$ of $R$ is called a $phi-r$-ideal of $R$ if whenever $abin I$ and $Ann(a)=(0)$ imply that $bin I$ for each $a,bin R.$ In addition to giving many properties of $phi-r$-ideal, we also examine the concept of $phi-r$-ideal in trivial ring extension and use them to characterize total quotient rings." @default.
- W4287757367 created "2022-07-26" @default.
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- W4287757367 date "2020-06-15" @default.
- W4287757367 modified "2023-10-16" @default.
- W4287757367 title "Generalizations of r-ideals of commutative rings" @default.
- W4287757367 doi "https://doi.org/10.48550/arxiv.2006.12261" @default.
- W4287757367 hasPublicationYear "2020" @default.
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