Ideal structure of Hurwitz series rings.
Benhissi, Ali (2007)
Beiträge zur Algebra und Geometrie
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Benhissi, Ali (2007)
Beiträge zur Algebra und Geometrie
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Fiedler, Bernd (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
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Sharma, R.K., Srivastava, J.B., Khan, Manju (2007)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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F. Azarpanah, O. Karamzadeh, A. Rezai Aliabad (1999)
Fundamenta Mathematicae
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An ideal I in a commutative ring R is called a z°-ideal if I consists of zero divisors and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We characterize topological spaces X for which z-ideals and z°-ideals coincide in , or equivalently, the sum of any two ideals consisting entirely of zero divisors consists entirely of zero divisors. Basically disconnected spaces, extremally disconnected and P-spaces are characterized in terms of z°-ideals....
Benjamin, E., Bresinsky, H. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Pchelintsev, S.V. (2007)
Sibirskij Matematicheskij Zhurnal
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Sabbaghan, Masoud, Shirazi, Fatemah Ayatollah Zadeh (2001)
International Journal of Mathematics and Mathematical Sciences
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Chernikov, N.S. (2002)
Sibirskij Matematicheskij Zhurnal
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M. Mulero (1996)
Fundamenta Mathematicae
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This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly non-noetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness criterion which is entirely analogous to the one for modules over principal ideal domains. ...
Kevin Hutchinson (1995)
Acta Arithmetica
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0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely...
Sereda, V. A., Filippov, V. T. (2002)
Sibirskij Matematicheskij Zhurnal
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Kilic, Nayil (2010)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Sabbaghan, Masoud, Shirazi, Fatemah Ayatollah Zadeh (2001)
International Journal of Mathematics and Mathematical Sciences
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Fiedler, Bernd (2001)
Séminaire Lotharingien de Combinatoire [electronic only]
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