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ساختارهای جبری مرتب

منابع و سر فصل

منابع:

1-                                                                                                                          Blyth. T. B., Lattices and Ordered Algebraic Structures,  2005

2-                                                                                       Birkhoff, G ., Lattice Theory, American Mathematical Society, Volume xxv, 1973  

3-                                                                                                                                                                 Gratzer., G., Lattice Theory: Foundation

سر فصل:

1- ( 3 جلسه)                           Ordered sets; residuated mappings; Closure; Isomorphism of Ordered sets; Galois connections  

2- ( 4 جلسه)                                                        Lattices; lattice morphism; Down-set lattices; Complete lattices

3- ( 3 جلسه)            Regular equivalences; Ordering quotient sets; Lattice congruences

4- ( 4 جلسه)                                                                             Modular lattices; Chain conditions; join-irreducibles

5- ( 4 جلسه)                                                               Distributive lattices prime ideals and filter

6- ( 4 جلسه)                                                 Complementation; boolean algebra; Stone,s representation theorem

7- (4 جلسه)                                                                 Pseudocomplementation; Stone and Heyting algebras

8- ( 3 جلسه)                                                                     Congruences; subdirectly irreducible algebras

9- ( 3 جلسه)                                                   groups; Archimedean ordered structures; Lattice ordered groups;

Totally ordered rings and fields