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ф-n-absorbing ideals and ф-generalized-n-absorbing ideals of commutative semirings |
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| รหัสดีโอไอ | |
| Title | ф-n-absorbing ideals and ф-generalized-n-absorbing ideals of commutative semirings |
| Creator | Pattarawan Petchkaew |
| Contributor | Amorn Wasanawichit, Sajee Pianskool |
| Publisher | Chulalongkorn University |
| Publication Year | 2558 |
| Keyword | Semirings (Mathematics), Rings (Algebra), เซมิริง, ริง (พีชคณิต) |
| Abstract | In this dissertation, we introduce the concepts of ф-primary ideals, ф-n-absorbing ideals and ф-generalized-n-absorbing ideals of a commutative semiring R with nonzero identity where ф is a function from the set of ideals of R into the set of ideals of R or the empty set. These are extended from primary ideals, n-absorbing ideals and generalized n-absorbing ideals of commutative rings with nonzero identity, respectively. We investigate ф-primary ideals, ф-n-absorbing ideals and ф-generalized-n-absorbing ideals in three types of semirings structures; namely, semirings (in general), quotient semirings and semirings of fractions in various points of view. In addition, we examine relationships among ф-primary ideals, ф-n-absorbing ideals and ф-generalized-n-absorbing ideals and can conclude that ф-primary ideals and ф-n-absorbing ideals do not imply each other; nevertheless, both imply ф-generalized-n-absorbing ideals. |
| URL Website | cuir.car.chula.ac.th |
