Basar, Abul; Abbasi, Mohammad Yahya On some powerful ideals of semigroups. (English) Zbl 1382.20054 Gulf J. Math. 5, No. 1, 102-107 (2017). Summary: Let \(S\) be a non trivial additive cancellation commutative semi-group having a zero 0 with the quotient group \(G=\{s_1-s_2\mid s_1,s_2\in S\}\). A prime ideal \(P\) of \(S\) is called strongly prime if for \(a,b\in G\), whenever \(a+b\in P\), we get \(a\in P\) or \(b\in P\). We show that a prime ideal of \(S\) is strongly prime \(\Leftrightarrow\) it is powerful. Finally, we prove that if \(O\) is an oversemigroup of \(S\) and \(S\) and \(O\) have the nonzero ideal \(I\) where \(I\) is powerful in \(O\), then \(3I\) is a powerful ideal of \(S\). MSC: 20M12 Ideal theory for semigroups 20M14 Commutative semigroups Keywords:semigroups; powerful ideals; strongly prime ideals PDFBibTeX XMLCite \textit{A. Basar} and \textit{M. Y. Abbasi}, Gulf J. Math. 5, No. 1, 102--107 (2017; Zbl 1382.20054) Full Text: Link