#### Glasnik Matematicki, Vol. 42, No.2 (2007), 301-308.

### THE IDEAL THEORY IN THE QUOTIENTS OF SEMIRINGS

### Shahabaddin Ebrahimi Atani

Department of Mathematics, University of Guilan,
P.O. Box 1914, Rasht, Iran

**Abstract.** Since the theory of ideals plays an important role in the
theory of quotient semirings, in this paper, we will make an intensive
study of the notions of Noetherian, Artinian, prime, primary, weakly primary
and *k*-maximal ideals in commutative quotient semirings. The bulk of this
paper is devoted to stating and proving analogues to several well-known
theorems in the theory of the residue class rings.

**2000 Mathematics Subject Classification.**
16Y60.

**Key words and phrases.** Semiring, *k*-ideals, *Q*-ideals, quotient semiring.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.42.2.05

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