In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

in this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

We prove that when the number of (potential) buyers is at least three, every ex post equilibrium in the Vickrey-Clarke-Groves combinatorial auction mechanisms is a bundling equilibrium and is symmetric. This complements a theorem proved in Holzman, Kfir-Dahav, Monderer, and Tennenholtz [6], according to which, the symmetric bundling equilibria are precisely those defined by a quasi field.