Subtractive extension of ideals in semirings | Zendy

J. N. Chaudhari | Zendy; Bijan Davvaz | Zendy; Kunal Julal Ingale | Zendy

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Subtractive extension of ideals in semirings

Author(s) -

J. N. Chaudhari,

Bijan Davvaz,

Kunal Julal Ingale

Publication year - 2014

Publication title -

sarajevo journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 2233-1964

pISSN - 1840-0655

DOI - 10.5644/sjm.10.1.02

Subject(s) - extension (predicate logic) , subtractive color , mathematics , algebra over a field , pure mathematics , programming language , computer science , art , visual arts

In this paper, we (1) obtain the k-closure of ideals and a characterization of subtractive extension of ideals in the semiring Z + ; (2) introduce the concept of closure of an ideal A of a semiring R with respect to an ideal I of R and prove the set of all subtractive extensions of an ideal I of a semiring R is a complete lattice; (3) show that a subtractive extension P of a Q-ideal I in a semiring R is a semiprime ideal if and only if P=I(Q\P) is a semiprime ideal in the quotient semiring R=I(Q):

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