Affiliation:
1. Department of Mathematics Yasouj University Yasouj Iran
2. Department of Mathematical Sciences Yazd University Yazd Iran
Abstract
Abstract
In this paper, we first give a topological representation of some algebraic lattices of ideals of C(X). Next, we apply these results and prove that a space X is normal if and only if the lattice of closed fixed ideals of C(X) is a sublattice of the lattice of ideals of C(X). It is proved that if two rings C(X) and C(Y) are isomorphic, then two lattices Z
∘[X] and Z
∘[Y] are isomorphic. We conclude that two rings C
*(X) and C
*(Y) are isomorphic if and only if two lattices Z[βX] and Z[βY] are isomorphic.