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Structure of unit groups of quotient rings of integers in Some cubic fields |
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| รหัสดีโอไอ | |
| Title | Structure of unit groups of quotient rings of integers in Some cubic fields |
| Creator | Pitchayatak Ponrod |
| Contributor | Ajchara Harnchoowong |
| Publisher | Chulalongkorn University |
| Publication Year | 2559 |
| Keyword | Rings (Algebra), Quotient rings, ริง (พีชคณิต), ริงผลหาร |
| Abstract | In the ring of integer ℤ, the structure of unit groups of quotient rings, denoted by (ℤn)×, is known. By the Chinese remainder theorem, the study of structure of (ℤn)× is reduced to study the structure of (ℤpe)× for all primes p and natural numbers e. It is well known that for an odd prime p, (ℤpe)× is a cyclic group of order ϕ(pe) for all natural number e, while (ℤ₂)× = {1}, (ℤ₄)× = <−1> and (ℤ₂e)× = <−1> × <5> for all natural numbers e ≥ 3. For a number field K, denote the ring of integers in K by OK. In this thesis we will study the structure of unit groups of quotient rings, denoted by (OK/A)×, for any ideal A of OK for cubic fields K with square-free discriminant. |
| URL Website | cuir.car.chula.ac.th |
