PEMBUKTIAN AUTOMORFISMA PADA GELANGGANG POLINOM MIRING UNTUK PEMBENTUKAN GELANGGANG POLINOM MIRING BERSUSUN

Amir Kamal Amir

Abstract


Let R be any ring with identity 1, 𝜎1 be an endomorphism of R and 𝛿 derivation. The skew polynomialΒ  ring over R in an indeterminate π‘₯ 1, denoted by 𝑅[π‘₯],Β  is the set of polynomials π‘Žπ‘› π‘₯1 𝑛 + π‘Ž 𝑛 βˆ’1 π‘₯ 1 𝑛 βˆ’1 + β‹― + π‘Ž 0Β  where π‘Ž ∈ 𝑅  with multiplication rule π‘₯ 1 π‘Ž = 𝜎 1 π‘Ž π‘₯ 1 + 𝛿1 𝑖 (π‘Ž)Β Β  for all π‘Ž ∈ 𝑅.Β  In this paper, it will be proved an automorphism 𝜎 on the skew polynomial ring 𝑅[π‘₯ 1 ; 𝜎 1 , 𝛿 ],Β  such that with that automorphism we can construct a iterated skew polynomial ringΒ  with variabel π‘₯1 and π‘₯2, i.e., 𝑅[π‘₯1;𝜎1;𝛿1][π‘₯2;𝜎2].

Keywords


automorphism; ring; iterated; skew; polynomial

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ISSN 1829-5266 (print) | ISSN 2301-8550 (online)
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