Boolean Algebras: Boolean Algebras and De Morgan formulae – complete Boolean algebras - Boolean Algebras and Boolean Rings – valuation of Boolean algebras. Semimodular lattices: Birkhoff lattices – semimodular lattices – equivalence lattices – linear dependence - complemented semimodular lattices. Ideals of Lattices: Ideals and Dual Ideals of lattices – Ideal Chains– Ideal lattices – Distributive lattices and rings of sets. Congruence Relations: Congruence relations of an algebra - Permutable equivalence relations –The Schreier refinement theorem - Congruence relations of lattices - minimal congruence relations of some subsets of a distributive lattice - Connection between Ideals and Congruence relations of a lattice. Direct and subdirect decompositions: Direct sum and subdirect union of lattices - Direct sum and subdirect decompositions of lattices – Neutral elements and center of a lattice.
- Teacher: Radhakrishna Kishore