Permutation groups, pattern involvement, and Galois connections
نویسندگان
چکیده
منابع مشابه
Galois Groups as Permutation Groups
Writing f(T ) = (T − r1) · · · (T − rn), the splitting field of f(T ) over K is K(r1, . . . , rn). Each σ in the Galois group of f(T ) over K permutes the ri’s since σ fixes K and therefore f(r) = 0⇒ f(σ(r)) = 0. The automorphism σ is completely determined by its permutation of the ri’s since the ri’s generate the splitting field over K. A permutation of the ri’s can be viewed as a permutation ...
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Writing f(X) = (X− r1) · · · (X− rn), the splitting field of f(X) over K is K(r1, . . . , rn). Each σ in the Galois group of f(X) over K permutes the ri’s since σ fixes K and therefore f(r) = 0⇒ f(σ(r)) = 0. The automorphism σ is completely determined by its permutation of the ri’s since the ri’s generate the splitting field over K. A permutation of the ri’s can be viewed as a permutation of th...
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Most studies of Galois connections begin with a function and ask the question: when is there a second function that is connected to the first? In possibly the very first application of Galois connections directly related to the modern digital computer, Hartmanis and Stearns posed a. subtly different question, namely: when does a relation define two functions that are Ga'!ois connected? Such a r...
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ژورنال
عنوان ژورنال: Acta Scientiarum Mathematicarum
سال: 2017
ISSN: 0001-6969
DOI: 10.14232/actasm-017-510-4