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### ON (α,β)-SKEW-COMMUTING AND (α,β)-SKEW-CENTRALIZING MAPS IN RINGS WITH LEFT IDENTITY

JUNG, YONG-SOO   (Department of Mathematics Chungnam National UniversityUU0001302  ); CHANG, ICK-SOON   (Department of Mathematics Chungnam National UniversityUU0001302  );
• #### 초록

Let R be a ring with left identity. Let G : $R{\times}R{\to}R$ be a symmetric biadditive mapping and g the trace of G. Let ${\alpha}\;:\;R{\to}R$ be an endomorphism and ${\beta}\;:\;R{\to}R$ an epimorphism. In this paper we show the following: (i) Let R be 2-torsion-free. If g is ( ${\alpha},{\beta}$ )-skew-commuting on R, then we have G = 0. (ii) If g is ( ${\beta},{\beta}$ )-skew-centralizing on R, then g is ( ${\beta},{\beta}$ )-commuting on R. (iii) Let $n{\ge}2$ . Let R be (n+1)!-torsion-free. If g is n-( ${\alpha},{\beta}$ )-skew-commuting on R, then we have G = 0. (iv) Let R be 6-torsion-free. If g is 2-( ${\alpha},{\beta}$ )-commuting on R, then g is ( ${\alpha},{\beta}$ )-commuting on R.

• #### 주제어

rings with left identity.

• #### 참고문헌 (5)

1. H. E. Bell and J. Lucier, On additive maps and commutativity in rings, Results Math. 36 (1999), 1-8
2. H. E. Bell and Q. Deng, On ring epimorphisms with centralizing conditions, Chinese J. Math. 23 (1995), 67-78
3. M. Bresar, Commuting maps: a survey, Taiwanese J. Math., to appear
4. Q. Deng and H. E. Bell, On derivations and commutativity in semiprime rings, Comm. Algebra 23 (1995), 3705-3713
5. J. Vukman, Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. 109 (1990), 47-52
• #### 이 논문을 인용한 문헌 (1)

1. 2015. "" Kyungpook mathematical journal, 55(1): 1~12

저자의 다른 논문

• #### Jung, Yong-Soo (25)

1. 1993 "Results Concerning the Nilpotency of the Separating Ideal of a Banach Algebra" 충청수학회지 = Journal of the Chungcheong Mathematical Society 6 (1): 89~94
2. 1994 "Noncommutative Versions of Singer-Wermer Theorem" 충청수학회지 = Journal of the Chungcheong Mathematical Society 7 (1): 41~46
3. 1995 "LEFT DERIVATIONS ON BANACH ALGEBRAS" 충청수학회지 = Journal of the Chungcheong Mathematical Society 8 (1): 37~44
4. 1997 "A NOTE OF LEFT DERIVATIONS ON BANACH ALGEBRAS" Korean journal of computational & applied mathematics 4 (2): 555~561
5. 1998 "LINEAR JORDAN DERIVATIONS ON BANACH ALGEBRAS" Korean journal of computational & applied mathematics 5 (2): 539~546
6. 1998 "SYMMETRIC BI-DERIVATIONS IN PRIME RINGS" Korean journal of computational & applied mathematics 5 (3): 819~826
7. 1998 "ON LEFT DERIVATIONS AND DERIVATIONS OF BANACH ALGEBRAS" Bulletin of the Korean Mathematical Society = 대한수학회보 35 (4): 659~667
8. 1998 "ON DERIVATIONS IN NONCOMMUTATIVE SEMISIMPLE BANACH ALGEBRAS" Bulletin of the Korean Mathematical Society = 대한수학회보 35 (3): 583~590
9. 1999 "SPECTRALLY BOUNDED JORDAN DERIVATIONS ON BANACH ALGEBRAS" Bulletin of the Korean Mathematical Society = 대한수학회보 36 (3): 477~481
10. 2000 "RESULTS ON THE RANGE OF DERIVATIONS" Bulletin of the Korean Mathematical Society = 대한수학회보 37 (2): 265~272

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