On 2-absorbing ideals in commutative semirings
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2023-10-31 19:41
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512.558 (2)
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KUMAR, Pratibha, DUBEY, ManishKant, SAROHE, Poonam. On 2-absorbing ideals in commutative semirings. In: Quasigroups and Related Systems, 2016, vol. 24, nr. 1(35), pp. 67-74. ISSN 1561-2848.
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Quasigroups and Related Systems
Volumul 24, Numărul 1(35) / 2016 / ISSN 1561-2848

On 2-absorbing ideals in commutative semirings
CZU: 512.558

Pag. 67-74

Kumar Pratibha1, Dubey ManishKant2, Sarohe Poonam3
 
1 University of Delhi,
2 Defence Scientific Information & Documentation centre,
3 Lakshmibai College, University of Delhi
 
Disponibil în IBN: 3 august 2016


Rezumat

We study 2-absorbing ideals in a commutative semiring S with 1 6= 0 and prove some important results analogous to ring theory. More general form of the Prime Avoidance Theorem is also given. We also prove that if I = ha1; a2; : : : ; ari is a _nitely generated ideal of a semiring S and P1; P2; : : : ; Pn are subtractive prime ideals of S such that I * Pi for each 1 6 i 6 n, then there exist b2; : : : ; br 2 S such that c = a1 b2a2 : : : brar =2 nS i=1 Pi.