Note on rings in which every proper left-ideal is cyclic
F. Szász (1957)
Fundamenta Mathematicae
Similarity:
F. Szász (1957)
Fundamenta Mathematicae
Similarity:
Karim Samei (2006)
Fundamenta Mathematicae
Similarity:
In a commutative ring R, an ideal I consisting entirely of zero divisors is called a torsion ideal, and an ideal is called a z⁰-ideal if I is torsion and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We prove that in large classes of rings, say R, the following results hold: every z-ideal is a z⁰-ideal if and only if every element of R is either a zero divisor or a unit, if and only if every maximal ideal in R (in general, every prime z-ideal)...
F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2015)
Colloquium Mathematicae
Similarity:
Kulosman, H. (2009)
Acta Mathematica Universitatis Comenianae. New Series
Similarity:
David Rudd (1972)
Fundamenta Mathematicae
Similarity:
Kar, S. (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
Similarity:
M. Behboodi, A. Moradzadeh-Dehkordi (2012)
Archivum Mathematicum
Similarity:
In this paper we study commutative rings whose prime ideals are direct sums of cyclic modules. In the case is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring , the following statements are equivalent: (1) Every prime ideal of is a direct sum of cyclic -modules; (2) where is an index set and is a principal ideal ring for each ; (3) Every prime ideal of is a direct...
Nowak, Krzysztof Jan (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
Similarity:
Dobbs, David E. (2006)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Azzouz Cherrabi, Abderrahim Miri (1999)
Extracta Mathematicae
Similarity:
Chaopraknoi, Sureeporn, Savettaseranee, Knograt, Lertwichitsilp, Patcharee (2005)
General Mathematics
Similarity:
Chenglong Wu, Yuzhong Ding (2008)
Formalized Mathematics
Similarity:
In this article three classes of ideals are discussed: associative ideals, commutative ideals, implicative ideals and positive implicative ideals, and their elementary properties. Some of their properties and the relationships between them have not been proven yet, and will be completed in the following article.MML identifier: BCIIDEAL, version: 7.8.10 4.99.1005