سعید رسولی

‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎The ‎theory ‎of ‎systems ‎over ‎monoids ‎has ‎been ‎investigated ‎over ‎than ‎four ‎decades. ‎From ‎the ‎other ‎side‎ ‎such ‎algebraic ‎structures ‎endowed ‎with ‎orders, ‎have ‎been ‎investigated ‎as a‎ ‎generalization ‎of ‎systems,‎ which the class of such algebraic structures together with order and monoid action preserving mappings constitutes a category. ‎The ‎main ‎issue ‎in ‎this ‎thesis ‎concentrates ‎on ‎flatness ‎properties ‎of ‎indecomposable ‎S-posets ‎for a‎ ‎monoid ‎S, ‎in ‎particular ‎cyclic ‎S-posets. ‎In short, in this thesis ‎we ‎present ‎homological ‎classification ‎of ‎monoids ‎according ‎to ‎the ‎flatness ‎properties ‎of ‎indecomposable ‎S-posets.‎