Note on weakly 1-absorbing primary ideals
Filomat, Tome 36 (2022) no. 1, p. 165
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An ideal I of a commutative ring R is called a weakly primary ideal of R if whenever a, b ∈ R and 0 ab ∈ I, then a ∈ I or b ∈ √ I. An ideal I of R is called weakly 1-absorbing primary if whenever nonunit elements a, b, c ∈ R and 0 abc ∈ I, then ab ∈ I or c ∈ √ I. In this paper, we characterize rings over which every ideal is weakly 1-absorbing primary (resp. weakly primary). We also prove that, over a non-local reduced ring, every weakly 1-absorbing primary ideals is weakly primary
Classification :
13A15, 13F05
Keywords: Prime ideal, Primary ideal, 1-Absorbing primary ideal, Weakly primary ideal, Weakly 1-absorbing primary ideal
Keywords: Prime ideal, Primary ideal, 1-Absorbing primary ideal, Weakly primary ideal, Weakly 1-absorbing primary ideal
Fuad Ali Ahmed Almahdi; Mohammed Tamekkante; Ali N A Koam. Note on weakly 1-absorbing primary ideals. Filomat, Tome 36 (2022) no. 1, p. 165 . doi: 10.2298/FIL2201165A
@article{10_2298_FIL2201165A,
author = {Fuad Ali Ahmed Almahdi and Mohammed Tamekkante and Ali N A Koam},
title = {Note on weakly 1-absorbing primary ideals},
journal = {Filomat},
pages = {165 },
year = {2022},
volume = {36},
number = {1},
doi = {10.2298/FIL2201165A},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2201165A/}
}
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