On properties of fuzzy left \(h\)-ideals in hemirings with \(t\)-norms. (Q2368433)

Between semirings and rings lie hemirings. In order to copy the idea of ideals in rings, ideals in semirings defined analogously are often inadequate and extra conditions must be provided, e.g., \(k\)-ideals for semirings and \(h\)-ideals for hemirings. To fuzzify the notion of ideal, \(k\)-ideal, \(h\)-ideal in their appropriate setting standard methods are employable. Strengthening these notions further one may introduce a \(t\)-norm (as done here), an \(s\)-norm (not done here), or use intuitionistic fuzzification (also not done here) and proceed to develop a theory of the resulting class of ideals. In this paper the exact class is the class of (finite-valued, imaginable) \(T\)-fuzzy left \(h\)-ideals on hemirings \(S\) with \(t\)-norms is discussed and taken through its paces successfully including the observation (proven) that every \(T\)-fuzzy left \(h\)-ideal of an \(h\)-Noetherian hemiring is finite valued and that otherwise the expected behavior with respect to direct products and homomorphisms occurs also.