Joe Stickles - Academia.edu (original) (raw)

Uploads

Papers by Joe Stickles

Research paper thumbnail of Factorizations in self-idealizations of PIRs and UFRs

Bollettino dell'Unione Matematica Italiana, 2016

Research paper thumbnail of Using Reading Assignments in Teaching Calculus

Mathematics and Computer Education, 2008

Research paper thumbnail of Commutative Rings with Finitely Generated Multiplicative Semigroup

Research paper thumbnail of Resequencing Calculus with an Early Multivariate Approach

Research paper thumbnail of The Effect of Reading Assignments on Test Question Performance in Calculus

Mathematics and Computer Education, Oct 1, 2010

Research paper thumbnail of Properties of U-factorizations

Research paper thumbnail of Cut Vertices in Zero-Divisor Graphs of Finite Commutative Rings

Http Dx Doi Org 10 1080 00927872 2010 488681, Jun 1, 2011

Research paper thumbnail of Commutative Rings with Domain-type Properties

Research paper thumbnail of Properties of domainlike rings

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.

Research paper thumbnail of Zero-divisor graphs of direct products of commutative rings

Houston journal of mathematics

Research paper thumbnail of Zero-divisor ideals and realizable zero-divisor graphs

Involve, a Journal of Mathematics, 2009

Research paper thumbnail of Zero-divisor graphs in commutative rings

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.

Research paper thumbnail of Commutative Rings with Finitely Generated Multiplicative Semigroup

Research paper thumbnail of When are Associates Unit Multiples?

Rocky Mountain Journal of Mathematics, 2004

Research paper thumbnail of Survey Article: Graphical representations of factorizations in commutative rings

Rocky Mountain Journal of Mathematics, 2013

Research paper thumbnail of Zero-divisor graphs of idealizations

Journal of Pure and Applied Algebra, 2006

Research paper thumbnail of Zero-Divisor Graphs of Polynomials and Power Series Over Commutative Rings

Communications in Algebra, 2005

Research paper thumbnail of Cut Vertices in Zero-Divisor Graphs of Finite Commutative Rings

Communications in Algebra, 2011

Research paper thumbnail of Irreducible Divisor Graphs in Commutative Rings with Zero Divisors

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.

Research paper thumbnail of Irreducible Divisor Graphs and Factorization Properties of Domains

Communications in Algebra, 2011

Research paper thumbnail of Factorizations in self-idealizations of PIRs and UFRs

Bollettino dell'Unione Matematica Italiana, 2016

Research paper thumbnail of Using Reading Assignments in Teaching Calculus

Mathematics and Computer Education, 2008

Research paper thumbnail of Commutative Rings with Finitely Generated Multiplicative Semigroup

Research paper thumbnail of Resequencing Calculus with an Early Multivariate Approach

Research paper thumbnail of The Effect of Reading Assignments on Test Question Performance in Calculus

Mathematics and Computer Education, Oct 1, 2010

Research paper thumbnail of Properties of U-factorizations

Research paper thumbnail of Cut Vertices in Zero-Divisor Graphs of Finite Commutative Rings

Http Dx Doi Org 10 1080 00927872 2010 488681, Jun 1, 2011

Research paper thumbnail of Commutative Rings with Domain-type Properties

Research paper thumbnail of Properties of domainlike rings

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.

Research paper thumbnail of Zero-divisor graphs of direct products of commutative rings

Houston journal of mathematics

Research paper thumbnail of Zero-divisor ideals and realizable zero-divisor graphs

Involve, a Journal of Mathematics, 2009

Research paper thumbnail of Zero-divisor graphs in commutative rings

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.

Research paper thumbnail of Commutative Rings with Finitely Generated Multiplicative Semigroup

Research paper thumbnail of When are Associates Unit Multiples?

Rocky Mountain Journal of Mathematics, 2004

Research paper thumbnail of Survey Article: Graphical representations of factorizations in commutative rings

Rocky Mountain Journal of Mathematics, 2013

Research paper thumbnail of Zero-divisor graphs of idealizations

Journal of Pure and Applied Algebra, 2006

Research paper thumbnail of Zero-Divisor Graphs of Polynomials and Power Series Over Commutative Rings

Communications in Algebra, 2005

Research paper thumbnail of Cut Vertices in Zero-Divisor Graphs of Finite Commutative Rings

Communications in Algebra, 2011

Research paper thumbnail of Irreducible Divisor Graphs in Commutative Rings with Zero Divisors

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.

Research paper thumbnail of Irreducible Divisor Graphs and Factorization Properties of Domains

Communications in Algebra, 2011

Log In