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Publications (10 of 22) Show all publications
Gottlieb, C. (2020). FINITE UNIONS OF OVERRINGS OF AN INTEGRAL DOMAIN. Journal of Commutative Algebra, 12(1), 87-90
Open this publication in new window or tab >>FINITE UNIONS OF OVERRINGS OF AN INTEGRAL DOMAIN
2020 (English)In: Journal of Commutative Algebra, ISSN 1939-0807, E-ISSN 1939-2346, Vol. 12, no 1, p. 87-90Article in journal (Refereed) 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.

Keywords
integral domains, overrings, finite unions, avoidance
National Category
Mathematics
Identifiers
urn:nbn:se:su:diva-182913 (URN)10.1216/jca.2020.12.87 (DOI)000533547700006 ()
Available from: 2020-06-27 Created: 2020-06-27 Last updated: 2022-02-26Bibliographically approved
Gottlieb, C. (2017). Strongly prime ideals and strongly zero-dimensional rings. Journal of Algebra and its Applications, 16(10), Article ID 1750191.
Open this publication in new window or tab >>Strongly prime ideals and strongly zero-dimensional rings
2017 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 16, no 10, article id 1750191Article in journal (Refereed) 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.

Keywords
Prime ideal, zero-dimensional ring, intersections of ideals, strongly prime, strongly zero-dimensional, strongly, n-regular ring
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-138937 (URN)10.1142/S0219498817501912 (DOI)000411342000011 ()
Available from: 2017-01-30 Created: 2017-01-30 Last updated: 2022-02-28Bibliographically approved
Gottlieb, C. (2015). Finite unions of submodules. Communications in Algebra, 43(2), 847-855
Open this publication in new window or tab >>Finite unions of submodules
2015 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, no 2, p. 847-855Article in journal (Refereed) 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.

Keywords
ideal, ring, union
National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-109702 (URN)10.1080/00927872.2013.851204 (DOI)000348438100035 ()
Available from: 2014-11-27 Created: 2014-11-27 Last updated: 2022-02-23Bibliographically approved
Gottlieb, C. (2015). The Nakayama Property of a Module and Related Concepts. Communications in Algebra, 43(12), 5131-5140
Open this publication in new window or tab >>The Nakayama Property of a Module and Related Concepts
2015 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, no 12, p. 5131-5140Article in journal (Refereed) 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. 

Keywords
Nakayama property, maximal property, module
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-119935 (URN)10.1080/00927872.2014.958849 (DOI)000361540800008 ()
Available from: 2015-08-28 Created: 2015-08-28 Last updated: 2022-02-23Bibliographically approved
Gottlieb, C. (1999). The simple and straightforward construction of the regular 257-gon. The Mathematical intelligencer, 21(1), 31-37
Open this publication in new window or tab >>The simple and straightforward construction of the regular 257-gon
1999 (English)In: The Mathematical intelligencer, ISSN 0343-6993, E-ISSN 1866-7414, Vol. 21, no 1, p. 31-37Article in journal (Refereed) Published
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-93855 (URN)
Available from: 2013-09-18 Created: 2013-09-18 Last updated: 2022-02-24
Gottlieb, C. (1998). Modules covered by finite unions of submodules. Communications in Algebra, 26(7), 2351-2359
Open this publication in new window or tab >>Modules covered by finite unions of submodules
1998 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 26, no 7, p. 2351-2359Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Marcel Dekker, 1998
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-83864 (URN)
Available from: 2012-12-14 Created: 2012-12-14 Last updated: 2022-02-24
Gottlieb, C. (1997). Length and dimension modulo a Serre category. Communications in Algebra, 25(5), 1553-1561
Open this publication in new window or tab >>Length and dimension modulo a Serre category
1997 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 25, no 5, p. 1553-1561Article in journal (Refereed) Published
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-93854 (URN)
Available from: 2013-09-18 Created: 2013-09-18 Last updated: 2022-02-24
Gottlieb, C. (1996). On ideals which are almost zero, and related concepts. Communications in Algebra, 24(6), 2201-2209
Open this publication in new window or tab >>On ideals which are almost zero, and related concepts
1996 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 24, no 6, p. 2201-2209Article in journal (Refereed) Published
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-93853 (URN)
Available from: 2013-09-18 Created: 2013-09-18 Last updated: 2022-02-24
Gottlieb, C. (1995). A proof that commutative Artinian rings are Noetherian. Communications in Algebra, 23(12), 4687-4691
Open this publication in new window or tab >>A proof that commutative Artinian rings are Noetherian
1995 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 23, no 12, p. 4687-4691Article in journal (Refereed) Published
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-93852 (URN)
Available from: 2013-09-18 Created: 2013-09-18 Last updated: 2022-02-24Bibliographically approved
Gottlieb, C. (1995). Bounding the number of generators for a class of ideals in local rings. Communications in Algebra, 23(4), 1499-1502
Open this publication in new window or tab >>Bounding the number of generators for a class of ideals in local rings
1995 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 23, no 4, p. 1499-1502Article in journal (Refereed) Published
Keywords
ideal, local ring, generators
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:su:diva-93851 (URN)
Available from: 2013-09-18 Created: 2013-09-18 Last updated: 2022-02-24Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9932-3114

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