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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2018.1
- 수록면
- 615 - 621 (7page)
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Let R be a ring with the unity 1, and let e be an idempo- tent of R. In this paper, we discuss some symmetric property for the set {(a1, a2, ..., an) ∈ Rn : a1a2 · · · an = e}. We here investigate some properties of those rings with such a symmetric property for an arbitrary idempotent e; some of our results turn out to generalize some known re- sults observed already when n = 2 and e = 0, 1 by several authors. We also focus especially on the case when n = 3 and e = 1. As consequences of our observation, we also give some equivalent conditions to the commutativity for some classes of rings, in terms of the symmetric property.
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참고문헌 (4)
참고문헌 신청
D. D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27:2847~2852
P.M. Cohn / 1999 / Reversible rings / Bull. London Math. Soc. 31:641~648
J. Krempa / 1977 / Rings in which annihilators are ideals and their application to semigroup rings / Bull. Acad. Polon. Sci., Math. Astronom. Phys. 25:851~856
T. Y. Lam / 1991 / A First Course in Noncommutative Rings / Springer-Verlag
P.M. Cohn / 1999 / Reversible rings / Bull. London Math. Soc. 31:641~648
J. Krempa / 1977 / Rings in which annihilators are ideals and their application to semigroup rings / Bull. Acad. Polon. Sci., Math. Astronom. Phys. 25:851~856
T. Y. Lam / 1991 / A First Course in Noncommutative Rings / Springer-Verlag
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