On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings
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Let R be a commutative semiring. We define a proper ideal I of R to be 2-absorbing (resp., weakly 2-absorbing) if abc ∈ I (resp., 0 ̸= abc ∈ I)implies ab ∈ I or ac ∈ I or bc ∈ I. We show that a weakly 2-absorbing ideal I with I3= 0 is 2-absorbing. We give a number of results concerning 2-absorbing and weakly 2-absorbing ideals and examples of weakly 2-absorbing ideals. Finally we define the concept of 0 −(1−,2−,3−)2- absorbing ideals of R and study the relationship among these classes of ideals of R.
Abstract
Let R be a commutative semiring. We define a proper ideal I of R to be 2-absorbing (resp., weakly 2-absorbing) if abc ∈ I (resp., 0 ̸= abc ∈ I)implies ab ∈ I or ac ∈ I or bc ∈ I. We show that a weakly 2-absorbing ideal I with I3= 0 is 2-absorbing. We give a number of results concerning 2-absorbing and weakly 2-absorbing ideals and examples of weakly 2-absorbing ideals. Finally we define the concept of 0 −(1−,2−,3−)2- absorbing ideals of R and study the relationship among these classes of ideals of R.
참고문헌 (18)
- P. J. Allen, "Ideal theory in semirings", 박사, pp.1967
- P. J. Allen, "A fundamental theorem of homomorphisms for semirings", Proc. Amer. Math. Soc., 21, pp.412~416 (1969)
- P. J. Allen, "Ideal theory in the semiring Z+", Publ. Math. Debrecen, 22, pp.219~224 (1975)
- Paul J. Allen, "Ideal Theory in Commutative A-semirings", Kyungpook Mathematical Journal, 46(2), pp.261~271 (2006), 경북대학교 자연과학대학 수학과
- A. Badawi, "On 2-absorbing ideals of commutative rings", Bull. Austral. Math. Soc., 75, pp.417~429 (2007)
- A. Badawi, "On weakly 2-absorbing ideals of commutative rings", Houston J. Math.
- I. Dolinka, "Minimal varieties of semirings with involution", Algebra Univ., 44, pp.143~151 (2000)
- S. Ebrahimi Atani, "The ideal theory in quotients of commutative semirings", Glasnik Mathematicki, 42(62), pp.301~308 (2007)
- S. Ebrahimi Atani, "On k-weakly primary ideals over semirings", Sarajevo J. Math., 3(15), pp.9~13 (2007)
- R. Ebrahimi Atani, "Ideal theory in commutative semirings", Bul. Acad. Stinte Repub. Mold. Mat., 2(57), pp.14~23 (2008)
- S. Ghosh, "A note on regularity in matrix semirings", Proc. Japan Acad., 44, pp.1~4 (2004)
- J. S. Golan, "Semirings and Their Applications" (1999), Kluwer Academic Publishers
- V. Gupta, "Some remarks on semirings", Radovi Matematicki, 12, pp.13~18 (2003)
- V. Gupta, "Right π-regular semirings", Sarajevo J. Math., 14(2), pp.3~9 (2006)
- V. Gupta, "Characterization of weakly prime subtractive ideals in semirings", Bull. Inst. Math. Acad. Sin. (N.S.), 3(2), pp.347~352 (2008)
- J. A. Huckaba, "Commutative rings with zero divisors" (1988), Dekker
- S. LaGrassa, "Semirings: Ideals and polynomials", 박사, pp.1995
- Pandarinathan Nandakumar, "1-(2-) Prime Ideals in Semirings", Kyungpook Mathematical Journal, 50(1), pp.117~122 (2010), 경북대학교 자연과학대학 수학과