Pop, Adina Some properties of idempotents of \((n,m)\)-semirings. (English) Zbl 1349.16089 Creat. Math. Inform. 23, No. 2, 235-242 (2014). Summary: In this paper, some properties of the additive and multiplicative idempotents of an \((n,m)\)-semiring are investigate. Unlike the usual semiring for \(n,m\geq 3\), we show that there is additively cancellative \((n,m)\)-semiring which has more additive idempotents. They are neutral elements of the \(n\)-ary operation, too. It also shows that there are multiplicatively cancellative \((n,m)\)-semiring which has at least two multiplicative neutral elements. In addition, we give some properties of subtractive ideal of \((n,m)\)-semiring, notion introduced by Y. Zhu [Algebra 2013, Article ID 272104 (2013; Zbl 1331.16042)], as an extension of the similar definition of usual semiring. Cited in 2 Documents MSC: 16Y99 Generalizations 20N15 \(n\)-ary systems \((n\ge 3)\) 17A42 Other \(n\)-ary compositions \((n \ge 3)\) 16Y60 Semirings Keywords:\(n\)-semigroups; \((n,m)\)-semirings; idempotents; subtractive ideals Citations:Zbl 1331.16042 PDFBibTeX XMLCite \textit{A. Pop}, Creat. Math. Inform. 23, No. 2, 235--242 (2014; Zbl 1349.16089)