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Publikasjoner (10 av 22) Visa alla publikasjoner
Gottlieb, C. (2020). FINITE UNIONS OF OVERRINGS OF AN INTEGRAL DOMAIN. Journal of Commutative Algebra, 12(1), 87-90
Åpne denne publikasjonen i ny fane eller vindu >>FINITE UNIONS OF OVERRINGS OF AN INTEGRAL DOMAIN
2020 (engelsk)Inngår i: Journal of Commutative Algebra, ISSN 1939-0807, E-ISSN 1939-2346, Vol. 12, nr 1, s. 87-90Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Let R be an integral domain, and let A, A(1), A(2), ..., A s be overrings of R, where A is of the form S-1 R, where S = R \ p1 boolean OR ... boolean OR p(n) for for some prime ideals p(i), and where each A(i), i >= 2, is of the form S-i(-1) R for some multiplicatively closed subset S-i of R. It is shown that if A subset of A(1) boolean OR ... boolean OR A(s), then A subset of A(i) for some i.

Emneord
integral domains, overrings, finite unions, avoidance
HSV kategori
Identifikatorer
urn:nbn:se:su:diva-182913 (URN)10.1216/jca.2020.12.87 (DOI)000533547700006 ()
Tilgjengelig fra: 2020-06-27 Laget: 2020-06-27 Sist oppdatert: 2022-02-26bibliografisk kontrollert
Gottlieb, C. (2017). Strongly prime ideals and strongly zero-dimensional rings. Journal of Algebra and its Applications, 16(10), Article ID 1750191.
Åpne denne publikasjonen i ny fane eller vindu >>Strongly prime ideals and strongly zero-dimensional rings
2017 (engelsk)Inngår i: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 16, nr 10, artikkel-id 1750191Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

A prime ideal p is said to be strongly prime if whenever p contains an intersection of ideals, p contains one of the ideals in the intersection. A commutative ring with this property for every prime ideal is called strongly zero-dimensional. Some equivalent conditions are given and it is proved that a zero-dimensional ring is strongly zero-dimensional if and only if the ring is quasi-semi-local. A ring is called strongly n-regular if in each ideal a, there is an element a such that x=ax for all x ∈ an. Connections between the concepts strongly zero-dimensional and strongly n-regular are considered.

Emneord
Prime ideal, zero-dimensional ring, intersections of ideals, strongly prime, strongly zero-dimensional, strongly, n-regular ring
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-138937 (URN)10.1142/S0219498817501912 (DOI)000411342000011 ()
Tilgjengelig fra: 2017-01-30 Laget: 2017-01-30 Sist oppdatert: 2022-02-28bibliografisk kontrollert
Gottlieb, C. (2015). Finite unions of submodules. Communications in Algebra, 43(2), 847-855
Åpne denne publikasjonen i ny fane eller vindu >>Finite unions of submodules
2015 (engelsk)Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, nr 2, s. 847-855Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

This paper is concerned with finite unions of ideals and modules. The first main result is that, if N ⊆ N 1 ∪N 2 ∪ … ∪ N s is a covering of a module N by submodules N i , such that all but two of the N i are intersections of strongly irreducible modules, then N ⊆ N k for some k. The special case when N is a multiplication module is considered. The second main result generalizes earlier results on coverings by primary submodules. In the last section unions of cosets is studied.

Emneord
ideal, ring, union
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-109702 (URN)10.1080/00927872.2013.851204 (DOI)000348438100035 ()
Tilgjengelig fra: 2014-11-27 Laget: 2014-11-27 Sist oppdatert: 2022-02-23bibliografisk kontrollert
Gottlieb, C. (2015). The Nakayama Property of a Module and Related Concepts. Communications in Algebra, 43(12), 5131-5140
Åpne denne publikasjonen i ny fane eller vindu >>The Nakayama Property of a Module and Related Concepts
2015 (engelsk)Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, nr 12, s. 5131-5140Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Three related properties of a module are investigated in this article, namely the Nakayama property, the Maximal property, and the S-property. A module M has the Nakayamapropertyif aM=M for an ideal a implies that sM=0 for some s∈a+1. A module M has the Maximal property if there is in M a maximal proper submodule, and finally, M is said to have the S-property if S^{−1}M = 0 for a multiplicatively closed set S implies that sM=0 for some s∈S. 

Emneord
Nakayama property, maximal property, module
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-119935 (URN)10.1080/00927872.2014.958849 (DOI)000361540800008 ()
Tilgjengelig fra: 2015-08-28 Laget: 2015-08-28 Sist oppdatert: 2022-02-23bibliografisk kontrollert
Gottlieb, C. (1999). The simple and straightforward construction of the regular 257-gon. The Mathematical intelligencer, 21(1), 31-37
Åpne denne publikasjonen i ny fane eller vindu >>The simple and straightforward construction of the regular 257-gon
1999 (engelsk)Inngår i: The Mathematical intelligencer, ISSN 0343-6993, E-ISSN 1866-7414, Vol. 21, nr 1, s. 31-37Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-93855 (URN)
Tilgjengelig fra: 2013-09-18 Laget: 2013-09-18 Sist oppdatert: 2022-02-24
Gottlieb, C. (1998). Modules covered by finite unions of submodules. Communications in Algebra, 26(7), 2351-2359
Åpne denne publikasjonen i ny fane eller vindu >>Modules covered by finite unions of submodules
1998 (engelsk)Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 26, nr 7, s. 2351-2359Artikkel i tidsskrift (Fagfellevurdert) Published
sted, utgiver, år, opplag, sider
Marcel Dekker, 1998
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-83864 (URN)
Tilgjengelig fra: 2012-12-14 Laget: 2012-12-14 Sist oppdatert: 2022-02-24
Gottlieb, C. (1997). Length and dimension modulo a Serre category. Communications in Algebra, 25(5), 1553-1561
Åpne denne publikasjonen i ny fane eller vindu >>Length and dimension modulo a Serre category
1997 (engelsk)Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 25, nr 5, s. 1553-1561Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-93854 (URN)
Tilgjengelig fra: 2013-09-18 Laget: 2013-09-18 Sist oppdatert: 2022-02-24
Gottlieb, C. (1996). On ideals which are almost zero, and related concepts. Communications in Algebra, 24(6), 2201-2209
Åpne denne publikasjonen i ny fane eller vindu >>On ideals which are almost zero, and related concepts
1996 (engelsk)Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 24, nr 6, s. 2201-2209Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-93853 (URN)
Tilgjengelig fra: 2013-09-18 Laget: 2013-09-18 Sist oppdatert: 2022-02-24
Gottlieb, C. (1995). A proof that commutative Artinian rings are Noetherian. Communications in Algebra, 23(12), 4687-4691
Åpne denne publikasjonen i ny fane eller vindu >>A proof that commutative Artinian rings are Noetherian
1995 (engelsk)Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 23, nr 12, s. 4687-4691Artikkel i tidsskrift (Fagfellevurdert) Published
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-93852 (URN)
Tilgjengelig fra: 2013-09-18 Laget: 2013-09-18 Sist oppdatert: 2022-02-24bibliografisk kontrollert
Gottlieb, C. (1995). Bounding the number of generators for a class of ideals in local rings. Communications in Algebra, 23(4), 1499-1502
Åpne denne publikasjonen i ny fane eller vindu >>Bounding the number of generators for a class of ideals in local rings
1995 (engelsk)Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 23, nr 4, s. 1499-1502Artikkel i tidsskrift (Fagfellevurdert) Published
Emneord
ideal, local ring, generators
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:su:diva-93851 (URN)
Tilgjengelig fra: 2013-09-18 Laget: 2013-09-18 Sist oppdatert: 2022-02-24bibliografisk kontrollert
Organisasjoner
Identifikatorer
ORCID-id: ORCID iD iconorcid.org/0000-0001-9932-3114