Weinert, H. J.; Sen, M. K.; Adhikari, M. R. One-sided \(k\)-ideals and \(h\)-ideals in semirings. (English) Zbl 0847.16033 Math. Pannonica 7, No. 1, 147-162 (1996). Let \((S,+,\cdot)\) be a semiring with commutative addition. A left ideal \(A\) of \(S\) is said to be a left \(k\)-ideal if \(a+a_1=a_2\) for some \(a_i\in A\) and \(a\in S\) implies \(a\in A\). A left ideal \(A\) of \(S\) is called a left \(h\)-ideal if \(a+a_1+u=a_2+u\) for some \(a_i\in A\) and \(u,a\in S\) implies \(a\in A\). Analogously we define two-sided \(k\)-ideals and \(h\)-ideals of \(S\).In this paper the authors give sufficient conditions on a semiring \(S\) such that each proper (left) \(k\)-ideal or each proper (left) \(h\)-ideal is contained in a maximal one. They deal with semiring-theoretical generalizations of the fact that ideal \(A\) of a ring \(A\) is a maximal ideal of \(R\) iff the congruence class ring \(R/A\) has only the trivial ideals. Reviewer: B.Pondělíček (Praha) Cited in 4 Documents MSC: 16Y60 Semirings 16D25 Ideals in associative algebras 20M12 Ideal theory for semigroups Keywords:left \(k\)-ideals; left \(h\)-ideals; semirings; maximal ideals; congruence class rings PDFBibTeX XMLCite \textit{H. J. Weinert} et al., Math. Pannonica 7, No. 1, 147--162 (1996; Zbl 0847.16033) Full Text: EuDML