In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

In this paper a bijection between the set of prime ideals of a Leavitt path algebra L K (E) and a certain set which involves maximal tails in E and the prime spectrum of K[x, x −1 ] is established. Necessary and sufficient conditions on the graph E so that the Leavitt path algebra L K (E) is primitive are also found.

in this paper, we introduce the notion of primal strong co-ideals and give some results involving them. it is shown thatsubtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.

In this paper, the relationships of induced L-convex spaces with L-hull operators, product spaces, and quotient are discussed. It is shown that structure exactly by convex structure. Moreover, sub-S1, sub- S2, S2 S3 separation axioms introduced in spaces. Some properties them investigated.

A game on a convex geometry is a real-valued function de®ned on the family L of the closed sets of a closure operator which satis®es the ®nite Minkowski±Krein±Milman property. If L is the Boolean algebra 2 N then we obtain a n-person cooperative game. We will introduce convex and quasi-convex games on convex geometries and we will study some properties of the core and the Weber set of these games.

An inequality between the number of coverings in the ordered set J(Con L) of join irreducible congruences on a lattice L and the size of L is given. Using this inequality it is shown that this ordered set can be computed in time O(n 2 log 2 n), where n = jLj. This paper is motivated by the problem of eeciently calculating and representing the congruence lattice Con L of a nite lattice L. Of cou...