한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)
- 제1권1호
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- Pages.1-6
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- 1994
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
A NOTE OF PI-RINGS WITH RESTRICTED DESCENDING
초록
In this paper, some properties for a PI-ring satisfying the descending chain condition on essential left ideals are studied: Let R be a ring with a polynomial identity satisfying the descending chain condition on essential ideals. Then all minimal prime ideals in R are maximal ideals. Moreover, if R has only finitely many minimal prime ideals, then R is left and right Artinian. Consequently, if every primeideal of R is finitely generated as a left ideal, then R is left and right Artinian. A finitely generated PI-algebra over a commutative Noetherian ring satisfying the descending chain condition on essential left ideals is a finite module over its center.(omitted)
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