Subgelanggang Komutatif maksimal dari Gelanggang Polinom Miring
filawati · Hasanuddin University Repository · 2015
ABSTRACT Let R be a ring with identity 1, ?? be an endomorphism of R and ?? is a ??-derivation. The Skew Polynomial Ring over R in an indeterminate x is: R[x;??,??]={f(x)=r_n x^n+???+r_0 |r_i???R} with multiplication rule xr=??(r)x+??(r), for all r???R. The multiplication rule resulted in skew polynomial ring R[x;??,??] is not commutative although R is commutative. On the other hand, there is a subset in the polynomial ring oblique commutes. Skew polynomial ring can load more than one subring who commutes, and from which it commutes subring there are maximum. It can be shown that R is a commutative subring maximum of the skew polynomial ring of R[x;??] if R commutative and ?? is of infinite order (??^n???1). In addition, it can also be shown that R is maximal commutative subring of R[x;??] if R commutative, R has characteristic zero and ?? is non-zero. Keywords: Skew polynomial ring, maximal commutativity ABSTRACT Let R be a ring with identity 1, ?? be an endomorphism of R and ?? is a ??-derivation. The Skew Polynomial Ring over R in an indeterminate x is: R[x;??,??]={f(x)=r_n x^n+???+r_0 |r_i???R} with multiplication rule xr=??(r)x+??(r), for all r???R. The multiplication rule resulted in skew polynomial ring R[x;??,??] is not commutative although R is commutative. On the other hand, there is a subset in the polynomial ring oblique commutes. Skew polynomial ring can load more than one subring who commutes, and from which it commutes subring there are maximum. It can be shown that R is a commutative subring maximum of the skew polynomial ring of R[x;??] if R commutative and ?? is of infinite order (??^n???1). In addition, it can also be shown that R is maximal commutative subring of R[x;??] if R commutative, R has characteristic zero and ?? is non-zero. Keywords: Skew polynomial ring, maximal commutativity