J4 ›› 2009, Vol. 44 ›› Issue (8): 58-61.

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S-Noetherianess of A+xB［［x］］

  

  1. College of Science and Information Engineering, Northwest Minority U niversity, Lanzhou 730030, Gansu, China
  • Received:2008-12-30 Online:2009-08-16 Published:2009-11-08
  • About author:JIAO Yujuan(1976-), female, lecturer, major in computational mathematics. Email:jsjyj@xbmu.edu.cn

Abstract:

Let A⊆Bbe an extension  of commutative rings with identity, x an indeterminate over B, R:=A+xB［［ x］］ and SA a given multiplicative set . It is shown that if ,(∩snA,n≥1)∩S≠Фfor each  s∈S  where  Scons ists of nonzerodivisors, then Ris SNoetherian if and only if  A is S-Noetherian and B is an  S -finite A-module. 

 

 

Key words: S-Noetherian rings; S-finite ideal; anti-Archimedean multiplicative set

CLC Number: 

  • O153.3
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