IJPAM: Volume 108, No. 3 (2016)

$\phi$-PRIMARY SUBTRACTIVE IDEALS IN SEMIRINGS

R. Safakish$^1$, F. Fatahi$^2$, M. Lotfi Parsa$^3$
$^{1,2}$University of Buali Sina
Hamadan, IRAN
$^3$Sayyed Jamaleddin Asadabadi University
Asadabad 6541835583, IRAN


Abstract. Let $R$ be a commutative semiring with identity. Let $\phi: I(R)\rightarrow I(R)\cup\{\emptyset\}$ be a function where $I(R)$ is the set of ideals of $R$. A proper ideal $I$ of $R$ is called $\phi$-primary if whenever $a,b\in R$, $ab\in I-\phi(I)$ implies that either $ a\in I$ or $b\in \sqrt{I}$. So if we take $\phi_\emptyset(I)=\emptyset$ (resp., $\phi_0(I)=0$), a $\phi$-primary ideal is primary (resp., weakly primary). In this paper we study the properties of several generalizations of primary ideals of $R$.

Received: December 31, 2015

AMS Subject Classification: 16Y60

Key Words and Phrases: semiring, $\phi$-primary ideal, subtractive ideal

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DOI: 10.12732/ijpam.v108i3.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 3
Pages: 629 - 633


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