on the lattice of filters of intuitionistic linear algebras

In this paper, we investigate the filter theory of intuitionistic linear algebra (il-algebra, in short) with emphasis on the lattice of filters of il-algebras and relationship between filters and congruences on il-algebras. we characterize the filter generated by a subset and give some related properties. the prime filter for il-algebras is characterized and the prime filter theorem for il-algebra is established. we get that the lattice (f(l), ⊆) of filters of an il-algebra l is algebraic, brouwerian, pseudocomplemented and endowed with the structure of heyting algebra. we prove that the lattice of congruences and that of filters of any il-algebra are isomorphic.