## Accomplishments by Jesse Elliott

### 2017

#### Publications:

- "Idempotent Plethories."
*Journal of Algebra*. Vol. 463 Oct 1, 2016. 33-79. (http://dx.doi.org/10.1016/j.jalgebra.2016.06.008)

### 2015

#### Publications:

- "Semistar Operations on Dedekind Domains."
*Communications in Algebra*. Vol. 43 No. 1 January 2015. 236-248. - "Netwon basis relations and applications to integer-valued polynomials and q-binomial coefficients."
*Integers*. Vol. 14 August 2014. 1-22. - "Factoring Formal Power Series Over Principal Ideal Domains."
*Transactions of the American Mathematical Society*. Vol. 366 No. 8 May 2014. 3997-4019. - "The Probability That Int_n(D) is Free."
*Commutative Algebra: Recent Advances in Commutative Rings, Integer- Valued Polynomials, and Polynomial Functions*. Edited by M. Fontana, S. Glaz, and S. Frisch. New York: Springer-Verlag, 2014. 133-151.

#### Other Activities:

*A Dualist Perspective on the Axiom of Constructibility*. Conference Talk. Special Session on History and Philosophy of Mathematics, 2015 Spring Eastern Sectional Meeting of the AMS. Georgetown University, Washington, D.C.. Mar 8, 2015.*Closure Operations in Commutative Algebra as Quantic Nuclei*. Conference talk: Special Session on Closure Operations in Commutative Algebra, 2015 Spring Eastern Sectional Meeting of the AMS. Georgetown University. Washington, D.C.. Mar 8, 2015.*Factoring Formal Power Series Over Z*. Seminar talk; Algebra/Number Theory/Combinatorics Seminar. Claremont Center for the Mathematical Sciences, Claremont, CA. Sep 30, 2014.*Factoring formal power series over Z*. Colloquium talk. Mathematics Colloquium, California State University, Chico. Sep 26, 2014.*Factoring formal power series over principal ideal domains*. Conference talk. 2014 Western Spring Sectional Meeting of the AMS, University of New Mexico. May 5, 2014.

### 2014

#### Publications:

- "Presentations and module bases of integer-valued polynomial rings."
*Journal of Algebra and Its Applications*. Vol. 12 No. 1 January 2013. 1-25.

#### Other Activities:

*Newton interpolation, generalized binomial coefficients, and integer-valued polynomials*. Conference talk. Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions, Graz, Austria. Dec 20, 2012.

### 2013

#### Other Activities:

*Witt vectors and generalizations*. Conference talk. Witt Vectors in Arithmetic, Geometry, and Topology, University of New Mexico. May 15, 2012.*Factoring formal power series over principal ideal domains*. Conference talk. Fourth International Conference on Mathematical Sciences 2012, Al Ain, United Arab Emirates. Mar 11, 2012.

### 2012

#### Publications:

- "Integer-valued polynomial rings, t-closure, and associated primes."
*Communications in Algebra*. Vol. 39 No. 11 November 2011. 4128-4147. - "Birings and plethories of integer-valued polynomials."
*Third International Meeting on Integer-Valued Polynomials (2010), Actes des Rencontres du CIRM*. Vol. 2 No. 2 December 2010. 53-58.

#### Other Activities:

*Algebra, number theory, and the philosophy of mathematics*. Sabbatical presentation. CSU Channel Islands, Graduate Mathematics Colloquium. Feb 22, 2012.*Presentations and regular bases of integer-valued polynomial rings*. Talk at Algebra Seminar. Universite' de Picardie Jules Verne. Oct 17, 2011.*Introduction to quantales*. Talk at Joint Math Meeting of Uni Padova and CSU Channel Islands. Universit`a degli Studi di Padova. Mar 25, 2011.*Introduction to integer-valued polynomial rings*. Talk at Joint Math Meeting of “Roma Tre” and CSU Channel Islands. Universit`a degli Studi “Roma Tre”. Mar 21, 2011.*Quantales and applications to ring theory*. Talk at Mathematics Colloquium. San Francisco State University. Mar 2, 2011.- "Research in Commutative Algebra and Number Theory." Faculty Development Mini-Grant, CSU Channel Islands. Three units of reassigned time. 2011.
- "Interdisciplinary Research in the Philosophy of Mathematics to Support Authoring a Text." Sabbatical leave, CSU Channel Islands. one semester paid leave. 2011.

### 2010

#### Exhibitions / Presentations:

- "t-closure and integer-valued polynomial rings." Presented to Algebra Seminar, University of Utah. Salt Lake City, UT. Oct 22, 2010.
- "Quantales and applications to ring theory." Presented to Mathematics Colloquium, New Mexico State University. Las Cruces, NM. Sep 16, 2010.
- "t-closure and integer-valued polynomial rings." Presented to Algebra Seminar, New Mexico State University. Las Cruces, NM. Sep 15, 2010.

#### Publications:

- "Functorial properties of star operations."
*Communications in Algebra*. Vol. 38 No. 5 Jan 1, 2010. 1466-1490.

#### Other Activities:

- "Mathematics, Engineering, Music, Art and Culture of Italy." Instructionally Related Activities Grant, CSU Channel Islands. $25,062. 2011.
*Biring and plethory structures on integer-valued polynomial rings*. Third International Meeting on Integer-Valued Polynomials and Problems in Commutative Algebra. Marseille, France. Nov 29, 2010.*Abstract ideal theory, ideal systems, and semistar operations*. Rome Commutative Ring Theory Days 2010. Rome, Italy. May 20, 2010.

### 2009

#### Exhibitions / Presentations:

- "Functorial properties of star operations." Presented to 2009 Fall Southeastern Meeting of the American Mathematical Society. Boca Raton, FL. Oct 30, 2009.
- "Integer-valued polynomial rings and t-linked extensions." Presented to 2008 Fez Conference on Commutative Algebra and Applications. Fez, Morocco. 2008.

#### Publications:

- "Some new approaches to integer-valued polynomial rings."
*Commutative Algebra and its Applications: Proceedings of the Fifth Interational Fez Conference on Commutative Algebra and Applications*. Edited by Fontana, Kabbaj, Olberding, and Swanson. New York: de Gruyter, 2009. 223-237.

### 2008

#### Publications:

- "Ring structures on groups of arithmetic functions."
*Journal of Number Theory*. Vol. 128 No. 4 April 2008. 709-730.

### 2007

#### Exhibitions / Presentations:

- "Rings of Integer-Valued Polynomials." Presented to Number Theory Seminar. University of California, Los Angeles. Feb 5, 2008.
- "Universal Characterizations of Integer-Valued Polynomial Rings." Presented to Abelian Groups and Modules over Commutative Rings. University of Connecticut. Jun 11, 2007.
- "Integer-Valued Polynomial Rings." Presented to CSUCI and University of Warsaw Joint Math Meeting. University of Warsaw, Poland. May 31, 2007.
- "Infinity: A Panel Discussion." with R. Christopher, G. Wood, and J. Fogg. Presented to Mathematics Colloquium. CSUCI. May 1, 2007.
- "Integer-Valued Polynomial Rings." Presented to Mathematics Colloquium. California State University, Dominguez Hills. Apr 11, 2007.

#### Publications:

- "Universal properties of integer-valued polynomial rings."
*Journal of Algebra*. Vol. 318 No. 1 December 2007. 68-92.

#### Other Activities:

- Reviewer. Mathematical Reviews. 2008.
- Reviewer. Mathematical Reviews. 2007.

### 2006

#### Exhibitions / Presentations:

- "The Science, Art, and Philosophy of Mathematics." Presented to CSUCI Mathematics Colloquium. California State University Channel Islands. Feb 22, 2007.
- "Integer-Valued Polynomial Rings." Presented to Claremont Colleges Mathematics Colloquium. Claremont McKenna College, CA. Feb 21, 2007.
- "A Functorial Approach to Integer-Valued Polynomial Rings." Presented to UCSB Algebra Seminar. UCSB. Nov 13, 2006.
- "Polynomials in Commutative Algebra." Presented to Centro de Investigacion en Matematicas, Universidad Autonoma del Estado de Hidalgo. Pachuca, Mexico. Mar 24, 2006.

#### Publications:

- "Binomial rings, integer-valued polynomials, and lambda-rings."
*Journal of Pure and Applied Algebra*. Vol. 207 No. 1 September 2006. 165-185. - "Constructing Witt-Burnside rings."
*Advances in Mathematics*. Vol. 203 2006. 319-363.

#### Other Activities:

- "Integer-Valued Polynomial Rings." Faculty Development Mini-Grant, CSUCI. 2007.
- "Integer-Valued Polynomial Rings." Faculty Development Mini-Grant, CSUCI. 2006.

### 2004

#### Exhibitions / Presentations:

- "Binomial RIngs." Paper delivered at International Symposium on Communative Rings and Monoids. Graz, Austia, September 2004.
- "Commutative Rings and their Modules." Presented to conference. Cortona, Italy. May 2004.
- "Introduction to Binomial Rings." Presented to California Lutheran University, California State University Channel Island, and Pepperdine University Mathematics Seminar. February 2004.

#### Other Activities:

- "Research in Commutative Algebra and Number Theory." Faculty Development Mini-Grant, California State University Channel Islands. 2004.
- "Research in Commutative Algebra and Number Theory." Martin V. Smith Faculty Innovation and Excellence Grant, CSUCI. 2004.
- "Research in Commutative Algebra and Number Theory." Faculty Development Mini-Grant, CSUCI. 2003.