Rees algebra over an ideal in t-rings

• Jyoti Singh ^[1] ; Shiv Datt Kumar ^[1]
  1. [1] Motilal Nehru National Institute of Technology

     Motilal Nehru National Institute of Technology

     India

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 4 ((April 2015) ), 2015, págs. 830-838
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.04.032
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• Resumen

  • If there exists a finitely generated module M over a tt-ring such that tM=AnnMttM=AnnMt and M/tMM/tM is of finite length, then we show that commutator ideal [q,q][q,q] is contained in tqtq, for some prime ideal q under certain conditions. Using this property, we discuss the Noetherian property of the Rees algebra of the prime ideal q in tt-ring and as an application we give an analogue of the Artin–Rees lemma for tt-rings.