본문 바로가기
HOME> 논문 > 논문 검색상세

논문 상세정보

Communications of the Korean Mathematical Society = 대한수학회논문집 v.25 no.3, 2010년, pp.349 - 364   SCOPUS
본 등재정보는 저널의 등재정보를 참고하여 보여주는 베타서비스로 정확한 논문의 등재여부는 등재기관에 확인하시기 바랍니다.

RING ENDOMORPHISMS WITH THE REVERSIBLE CONDITION

Baser, Muhittin    (DEPARTMENT OF MATHEMATICS KOCATEPE UNIVERSITY   ); Kaynarca, Fatma    (DEPARTMENT OF MATHEMATICS KOCATEPE UNIVERSITY   ); Kwak, Tai-Keun    (DEPARTMENT OF MATHEMATICS DAEJIN UNIVERSITY  );
  • 초록

    P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for a, $b\;{\in}\;R$ . Commutative rings and reduced rings are reversible. In this paper, we extend the reversible condition of a ring as follows: Let R be a ring and $\alpha$ an endomorphism of R, we say that R is right (resp., left) $\alpha$ -shifting if whenever $a{\alpha}(b)\;=\;0$ (resp., $\alpha{a)b\;=\;0$ ) for a, $b\;{\in}\;R$ , $b{\alpha}{a)\;=\;0$ (resp., $\alpha(b)a\;=\;0$ ); and the ring R is called $\alpha$ -shifting if it is both left and right $\alpha$ -shifting. We investigate characterizations of $\alpha$ -shifting rings and their related properties, including the trivial extension, Jordan extension and Dorroh extension. In particular, it is shown that for an automorphism $\alpha$ of a ring R, R is right (resp., left) $\alpha$ -shifting if and only if Q(R) is right (resp., left) $\bar{\alpha}$ -shifting, whenever there exists the classical right quotient ring Q(R) of R.


  • 주제어

    ring endomorphism .   reduced ring .   reversible ring .   trivial extension .   classical right quotient ring.  

  • 참고문헌 (21)

    1. E. P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470?473. 
    2. D. D. Anderson and V. Camillo, Semigroups and rings whose zero products commute, Comm. Algebra 27 (1999), no. 6, 2847?2852. 
    3. M. Ba¸ser, C. Y. Hong, and T. K. Kwak, On extended reversible rings, Algebra Colloq. 16 (2009), no. 1, 37?48. 
    4. M. Ba¸ser, T. K. Kwak, and Y. Lee, The McCoy condition on skew polynomial rings, Comm. Algebra 37 (2009), no. 11, 4026?4037. 
    5. P. M. Cohn, Reversible rings, Bull. London Math. Soc. 31 (1999), no. 6, 641?648. 
    6. J. M. Habeb, A note on zero commutative and duo rings, Math. J. Okayama Univ. 32 (1990), 73?76. 
    7. C. Y. Hong, N. K. Kim, and T. K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra 151 (2000), no. 3, 215?226. 
    8. C. Y. Hong, N. K. Kim, and T. K. Kwak, On skew Armendariz rings, Comm. Algebra 31 (2003), no. 1, 103?122. 
    9. C. Y. Hong, T. K. Kwak, and S. T. Rizvi, Extensions of generalized Armendariz rings, Algebra Colloq. 13 (2006), no. 2, 253?266. 
    10. D. A. Jordan, Bijective extensions of injective ring endomorphisms, J. London Math. Soc. (2) 25 (1982), no. 3, 435?448. 
    11. N. K. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), no. 2, 477?488. 
    12. N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), no. 1-3, 207?223. 
    13. J. Krempa, Some examples of reduced rings, Algebra Colloq. 3 (1996), no. 4, 289?300. 
    14. J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971), 359?368. 
    15. T. K. Lee and Y. Q. Zhou, Armendariz and reduced rings, Comm. Algebra 32 (2004), no. 6, 2287?2299. 
    16. J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, John Wiley & Sons Ltd., 1987. 
    17. L. Motais de Narbonne, Anneaux semi-commutatifs et uniseriels; anneaux dont les ideaux principaux sont idempotents, Proceedings of the 106th National Congress of Learned Societies (Perpignan, 1981), 71?73, Bib. Nat., Paris, 1982. 
    18. A. R. Nasr-Isfahani and A. Moussavi, Ore extensions of skew Armendariz rings, Comm. Algebra 36 (2008), no. 2, 508?522. 
    19. P. P. Nielsen, Semi-commutativity and the McCoy condition, J. Algebra 298 (2006), no. 1, 134?141. 
    20. M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14?17. 
    21. G. Y. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43?60. 

 저자의 다른 논문

  • Kwak, Tai-Keun (15)

    1. 2000 "ON RINGS WHOSE PRIME IDEALS ARE MAXIMAL" Bulletin of the Korean Mathematical Society = 대한수학회보 37 (1): 1~19    
    2. 2002 "ON THE MAXIMALITY OE PRIME IDEALS IN EXCHANGE RINGS" Communications of the Korean Mathematical Society = 대한수학회논문집 17 (3): 409~422    
    3. 2004 "NILRADICALS OF SKEW POWER SERIES RINGS" Bulletin of the Korean Mathematical Society = 대한수학회보 41 (3): 507~519    
    4. 2007 "EXTENSIONS OF EXTENDED SYMMETRIC RINGS" Bulletin of the Korean Mathematical Society = 대한수학회보 44 (4): 777~788    
    5. 2008 "GENERALIZED SEMI COMMUTATIVE RINGS AND THEIR EXTENSIONS" Bulletin of the Korean Mathematical Society = 대한수학회보 45 (2): 285~297    
    6. 2010 "ON QUASI-RIGID IDEALS AND RINGS" Bulletin of the Korean Mathematical Society = 대한수학회보 47 (2): 385~399    
    7. 2013 "MCCOY CONDITION ON IDEALS OF COEFFICIENTS" Bulletin of the Korean Mathematical Society = 대한수학회보 50 (6): 1887~1903    
    8. 2014 "REFLEXIVE PROPERTY SKEWED BY RING ENDOMORPHISMS" Korean Journal of mathematics 22 (2): 217~234    
    9. 2015 "INSERTION-OF-FACTORS-PROPERTY ON SKEW POLYNOMIAL RINGS" Journal of the Korean Mathematical Society = 대한수학회지 52 (6): 1161~1178    
    10. 2016 "CORRIGENDUM TO "REFLEXIVE PROPERTY ON IDEMPOTENTS" [BULL. KOREAN MATH. SOC. 50 (2013), NO. 6, 1957-1972]" Bulletin of the Korean Mathematical Society = 대한수학회보 53 (6): 1913~1915    

 활용도 분석

  • 상세보기

    amChart 영역
  • 원문보기

    amChart 영역

원문보기

무료다운로드
유료다운로드
  • 원문이 없습니다.

유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.

원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.

NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.

이 논문과 함께 출판된 논문 + 더보기