On rings with annihilator condition
| Autor: | Ahmad Moussavi, Rasul Mohammadi, Masoome Zahiri |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Pure mathematics Noncommutative ring Mathematics::Commutative Algebra General Mathematics Polynomial ring 010102 general mathematics Semiprime ring Local ring Artinian ring 0102 computer and information sciences 01 natural sciences Category of rings 010201 computation theory & mathematics Von Neumann regular ring 0101 mathematics Commutative algebra Mathematics |
| Zdroj: | Studia Scientiarum Mathematicarum Hungarica. 54:82-96 |
| ISSN: | 1588-2896 0081-6906 |
| DOI: | 10.1556/012.2017.54.1.1355 |
| Popis: | In this paper we study rings R with the property that every finitely generated ideal of R consisting entirely of zero divisors has a nonzero annihilator. The class of commutative rings with this property is quite large; for example, noetherian rings, rings whose prime ideals are maximal, the polynomial ring R[x] and rings whose classical ring of quotients are von Neumann regular. We continue to study conditions under which right mininjective rings, right FP-injective rings, right weakly continuous rings, right extending rings, one sided duo rings, semiregular rings and semiperfect rings have this property. |
| Databáze: | OpenAIRE |
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