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Communications of the Korean Mathematical Society = 대한수학회논문집 v.25 no.3, 2010년, pp.349 - 364   SCOPUS
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### 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)

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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

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