Manuel Reyes

Spring 2013 Courses

• Math 171A, Integral Calculus
• Math 200A (joint with Thom Pietraho), Introduction to Mathematical Reasoning
• Math 231 (joint with Thom Pietraho), Intermediate Linear Algebra

Students can access online course materials by logging in to Blackboard.

Manny's Research and Papers

My research interests lie in Ring Theory (both noncommutative and commutative rings) and Noncommutative Algebraic Geometry. I am also interested in cases where these ideas intersect with the study of operator algebras and category theory.

• Skew Calabi-Yau algebras and homological identities (with Daniel Rogalski and James J. Zhang), preprint. (Also available at arXiv:1302.0437.)
• Active lattices determine AW*-algebras (with Chris Heunen), preprint. (Also available at arXiv:1212.5778.)
• Sheaves that fail to represent matrix rings, preprint. (Also available at arXiv:1211.4005.)
• Diagonalizing matrices over AW*-algebras (with Chris Heunen), to appear in J. Funct. Anal. (Also available at arXiv:1208.5120.)
• Obstructing extensions of the functor Spec to noncommutative rings, Israel J. Math. 192 (2012), no. 2, 667--698. (Also available at arXiv:1101.2239.)
• Noncommutative generalizations of theorems of Cohen and Kaplansky, Algebr. Represent. Theory 15 (2012), no. 5, 933--975. (Also available at arXiv:1007.3701.)
• A one-sided Prime Ideal Principle for noncommutative rings, Journal of Algebra and Its Applications 9 (2010), no. 6, 877--919. (Also available at arXiv:0903.5295.)
• Oka and Ako Ideal Families in Commutative Rings (with T.Y. Lam), Rings, Modules, and Representations, 263--288, Contemp. Math., 480, Amer. Math. Soc., Providence, RI, 2009.
• A Prime Ideal Principle in commutative algebra (with T.Y. Lam), Journal of Algebra 319 (2008), no. 7., 3006--3027.

Links

• MathOverflow is a website that I enjoy.
• Center of Ring Theory and its Applications at Ohio University is a place that I would like to visit someday.