董学东.关于伪准素环的注记[J].数学研究及应用,1995,15(3):341~344
关于伪准素环的注记
A Note on Pseudo Primary Rings
投稿时间:1993-06-28  
DOI:10.3770/j.issn:1000-341X.1995.03.004
中文关键词:  
英文关键词:primary ideal  commutative ring.
基金项目:
作者单位
董学东 辽宁师范大学数学系 
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中文摘要:
      一个有单位元的交换环R称为伪准素环,如果R的每个非零理想都是某个准素理想之幂.本文证明了环R是伪准素环当且仅当R是准素环或R是两个域的直和或R是至多具有三个素理想的一维局部环,并且每个非零理想或是某个极小素理想之幂或是某个属于极大理想的准不比理想之幂.
英文摘要:
      A commutative ring with identity R is called a pseudo primary ring if eachnon-zero ideal of R is a power of a primary ideal. In this note we prove that a ring Ris a pseudo primary ring if and only if R is a primary ring or R is a direct sum of twofields or R is a one-dimensional local ring with at most three prime ideals in which eachnon-zero ideal is a power of a minimal prime ideal or is a power of some primary idealbelonging to the maximal ideal.
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