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9.4/5 (M)(a) UNIVERSAL ALGEBRA
UNIT I
Lattices, definition and examples, isomorphic lattices, examples, sub lattices, distributive lattices, modular lattices, complete lattices, equivalence relations and partitions, algebraic lattices, closure operators, algebraic closure operators
UNIT II
Universal algebra, definition and example, sub algebras, isomarphic algebras, algebraic lattices, and sub universes, the irredundant basis theorem, congruence, qoutient algebras
UNIT III
Homomorphism, homomorphism and isomorphism theorems, direct products, factor congruence’s, directly indecomposable algebras, sub direct products, simple algebras, sub directly irreducible algebras, class operators and varieties
UNIT IV
Terms, term algebra, free algebras, identities, birkhoffs theorem, malkev conditions, the center of an algebra, equational logic and fully invariant congruencies
Text book
[1] S.Burries and H.P.sankappanavar , A course in universal algebra, Springer- verlag,1981
References
[1] G.Gratzer, Universal algebra, second edition, Springe-Verlag,Newyork,1979
[2] P.M.Cohn, Universal algebra, Harper and Row,NY,1965
[3] B.Johnson, Topics in universal algebra, Lecture notes in mathematics,
vol.25, Springe-Verlag,1972
For more details, visit http://www.nannayauniversity.info/courses.html
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