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The symmetric ring property was due to Lambek and provided many useful results in relation with noncommutative ring theory. In this note we consider this property over centers, introducing symmetric-over-center. It is shown that symmetric and symmetric-over-center are independent of each other. The structure of symmetric-over-center ring is studied in relation to various radicals of polynomial rings.
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참고문헌 (8)
참고문헌 신청
S.A. Amitsur / 1954 / A general theory of radicals III / American J. Math 76:126~136
S.A. Amitsur / 1956 / Radicals of polynomial rings / Canad. J. Math 8:355~361
D.D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27:2847~2852
G.F. Birkenmeier / 1993 / Completely prime ideals and asso-ciated radicals / Proc. Biennial Ohio State-Denison Conference 1992 :102~129
V. Camillo / 2010 / Nilpotent ideals in polynomial and power series rings / Proc. Amer. Math. Soc 138:1607~1619
S.A. Amitsur / 1956 / Radicals of polynomial rings / Canad. J. Math 8:355~361
D.D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27:2847~2852
G.F. Birkenmeier / 1993 / Completely prime ideals and asso-ciated radicals / Proc. Biennial Ohio State-Denison Conference 1992 :102~129
V. Camillo / 2010 / Nilpotent ideals in polynomial and power series rings / Proc. Amer. Math. Soc 138:1607~1619
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