Abstract
The notions of quasi-ideals of rings and semigroups were introduced by Steinfeld (Acta Math. Acad. Sci. Hung. 4: 289-298, 1953 and Publ. Math. (Debr.) 4:262-275, 1956) respectively. The notion of Gamma-semigroups was introduced by Sen (Proceeding of International Symposium on Algebra and Its Applications, Decker Publication, New York, 1981). Further the notion of (m, n) ideals of semigroups was introduced by Lajos (Acta Sci. Math. 22: 217-222, 1961). Later on (m, n) quasi-ideals and (m, n) bi-ideals were widely studied in various algebraic structures viz. semigroups, rings and near-rings etc. In this paper we have defined (m, n) quasi-Gamma-ideal and (m, n) bi-Gamma-ideal in Gamma-semigroup. Including other results, we have shown that if Q is a minimal (m, n) quasi-Gamma-ideal in Gamma-semigroup S then intersection of minimal m-left Gamma-ideals and minimal n-right Gamma-ideals is again a minimal (m, n) quasi-Gamma-ideals.