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Crossed Product Algebras Over Dihedral Field Extensions, Kaitlyn Lee
Crossed Product Algebras Over Dihedral Field Extensions, Kaitlyn Lee
Undergraduate Honors Thesis Collection
Let F be the field of fractions of R, a ring of power series with coefficients in some field. Let K/F be a finite Galois extension, and assume the integral closure S of R in K is also a power series ring.
In this paper, we consider a construction from ring theory called a crossed product algebra and an associated function f: G × G →K called a cocycle that is used to define a multiplication operation for the crossed product algebra. Consider a crossed product algebra whose cocycle f takes values in S. We give a proof concerning which …