جستجوی مقالات مرتبط با کلیدواژه "galois correspondence" در نشریات گروه "علوم پایه"

Galois connection in category theory play an important role inestablish the relationships between different spatial structures. Inthis paper, we prove that there exist many interesting Galoisconnections between the category of Alexandroff $L$-fuzzytopological spaces, the category of reflexive $L$-fuzzyapproximation spaces and the category of Alexandroff $L$-fuzzyinterior (closure) spaces. This indicates that there is a closeconnection between the three structures.

Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the category (L,M)-WICS of (L,M)-fuzzy weakly induced convex spaces, are coreflective subcategories of (L,M)-CS. It is also proved that three isomorphic categories, namely, the category MCS of M-fuzzifying convex spaces, the category (L,M)-CGCS of (L,M)-fuzzy convex spaces induced by M-fuzzifying convex spaces and the category (L,M)-ICS of (L,M)-fuzzy induced convex spaces, are coreflective subcategories of both (L,M)-SCS and (L,M)-WICS.

In a previous paper, the second author established that, given finite fields $F < E$ and certain subgroups $C leq E^times$, there is a Galois connection between the intermediate field lattice ${L mid F leq L leq E}$ and $C$''s subgroup lattice. Based on the Galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product $C rtimes {Gal} (E/F)$. However, the analysis when $|F|$ is a Mersenne prime is more complicated, so certain cases were omitted from that paper.The present exposition, which is a reworking of the previous article, provides a uniform analysis over all the families, including the previously undetermined ones. In the group $Crtimes{rm Gal(E/F)}$, we use the Galois connection to calculate stabilizers of linear characters, and these stabilizers determine the full character degree set. This is shown for each subgroup $Cleq E^times$ which satisfies the condition that every prime dividing $|E^times: C|$ divides $|F^times|$.