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Papers by Joe Stickles
Bollettino dell'Unione Matematica Italiana, 2016
Mathematics and Computer Education, 2008
Mathematics and Computer Education, Oct 1, 2010
Http Dx Doi Org 10 1080 00927872 2010 488681, Jun 1, 2011
Tamkang Journal of Mathematics
In this paper we will examine properties of and relationships between rings that share some prope... more In this paper we will examine properties of and relationships between rings that share some properties with integral domains, but whose definitions are less restrictive. If R is a commutative ring with identity, we call R a domainlike ring if all zero-divisors of R are nilpotent, which is equivalent to (0) being primary. We exhibit properties of domainlike rings, and we compare them to présimplifiable rings and (hereditarily) strongly associate rings. Further, we consider idealizations, localizations, zero-divisor graphs, and ultraproducts of domainlike rings.
Houston journal of mathematics
Involve, a Journal of Mathematics, 2009
Commutative Algebra, 2010
This article surveys the recent and active area of zero-divisor graphs of commutative rings. Nota... more This article surveys the recent and active area of zero-divisor graphs of commutative rings. Notable algebraic and graphical results are given, followed by a historical overview and an extensive bibliography.
Rocky Mountain Journal of Mathematics, 2004
Rocky Mountain Journal of Mathematics, 2013
Journal of Pure and Applied Algebra, 2006
Communications in Algebra, 2005
Communications in Algebra, 2011
Communications in Algebra, 2008
ABSTRACT In their article “Irreducible Divisor Graphs”, Coykendall and Maney (20077. Coykendall ,... more ABSTRACT In their article “Irreducible Divisor Graphs”, Coykendall and Maney (20077. Coykendall , J. , Maney , J. ( 2007 ). Irreducible divisor graphs . Comm. Alg. 35 : 885 – 895 . [Taylor & Francis Online], [Web of Science ®]View all references) introduced the idea of irreducible divisor graphs of elements of a domain. We generalize this concept to commutative rings with zero divisors. In particular, the interplay of unique factoring and connected/complete graphs is explored. The diameter and girth of such graphs are also briefly discussed.
Communications in Algebra, 2011
Bollettino dell'Unione Matematica Italiana, 2016
Mathematics and Computer Education, 2008
Mathematics and Computer Education, Oct 1, 2010
Http Dx Doi Org 10 1080 00927872 2010 488681, Jun 1, 2011
Tamkang Journal of Mathematics
In this paper we will examine properties of and relationships between rings that share some prope... more In this paper we will examine properties of and relationships between rings that share some properties with integral domains, but whose definitions are less restrictive. If R is a commutative ring with identity, we call R a domainlike ring if all zero-divisors of R are nilpotent, which is equivalent to (0) being primary. We exhibit properties of domainlike rings, and we compare them to présimplifiable rings and (hereditarily) strongly associate rings. Further, we consider idealizations, localizations, zero-divisor graphs, and ultraproducts of domainlike rings.
Houston journal of mathematics
Involve, a Journal of Mathematics, 2009
Commutative Algebra, 2010
This article surveys the recent and active area of zero-divisor graphs of commutative rings. Nota... more This article surveys the recent and active area of zero-divisor graphs of commutative rings. Notable algebraic and graphical results are given, followed by a historical overview and an extensive bibliography.
Rocky Mountain Journal of Mathematics, 2004
Rocky Mountain Journal of Mathematics, 2013
Journal of Pure and Applied Algebra, 2006
Communications in Algebra, 2005
Communications in Algebra, 2011
Communications in Algebra, 2008
ABSTRACT In their article “Irreducible Divisor Graphs”, Coykendall and Maney (20077. Coykendall ,... more ABSTRACT In their article “Irreducible Divisor Graphs”, Coykendall and Maney (20077. Coykendall , J. , Maney , J. ( 2007 ). Irreducible divisor graphs . Comm. Alg. 35 : 885 – 895 . [Taylor & Francis Online], [Web of Science ®]View all references) introduced the idea of irreducible divisor graphs of elements of a domain. We generalize this concept to commutative rings with zero divisors. In particular, the interplay of unique factoring and connected/complete graphs is explored. The diameter and girth of such graphs are also briefly discussed.
Communications in Algebra, 2011