Peter Loth, Ph.D.
Professor of Mathematics
Dr. Peter Loth is the author of the book "Classifications of abelian groups and Pontrjagin duality'' and has published numerous articles in various journals and conference proceedings. Before joining Sacred Heart University in 1998, he held visiting positions at Case Western Reserve University and at Muskingum College. His areas of research include model-theoretic aspects of abelian group theory and the interaction between topology and abelian groups. Courses he taught include Modern College Mathematics, Calculus, Linear Algebra, Abstract Algebra, Real Analysis and The Art of Thinking. He has been team advisor for the international Mathematical Contest in Modeling (MCM) for over 10 years. Dr. Loth is a member of the American Mathematical Society.
Degrees and Certifications
- Ph.D., Wesleyan University
- M.S., University of Erlangen-Nürnberg, Germany
- Modern College Mathematics
- Calculus for Decision Making
- Calculus I, II and III
- Linear Algebra
- Abstract Algebra
- Mathematical Structures and Proofs
- Real Analysis
- Complex Analysis
- Senior Seminar in Mathematics
- The Art of Thinking
Research Interests & Grants
- College of Arts and Sciences Release Time (Sacred Heart University, 2003, 2005, 2010-2012)
- Sabbatical Leave (Sacred Heart University, 2007)
- University Research and Creativity Grant (Sacred Heart University, 2004)
His research interests include model-theoretic aspects of abelian group theory and the interaction between topology and abelian groups.
Honors, Awards & Fellowship
- Marquis Who’s Who in the World, 2011-2013
- Marquis Who’s Who in America, 2009-2013
- Faculty Scholarship Award (Sacred Heart University, 2001)
Publications and Presentations
- Classifications of Abelian Groups and Pontrjagin Duality, Algebra, Logic and Applications, Volume 10, Gordon and Breach Science Publishers, Amsterdam (1998).
- Abelian groups with partial decomposition bases in Lδ∞ω, Part I (with C. Jacoby, K. Leistner and L. Strüngmann), in Groups and Model Theory, Contemp. Math.,Vol. 576, Amer. Math. Soc., Providence, RI (2012), 163-175.
- Abelian groups with partial decomposition bases in Lδ∞ω, Part II (with C. Jacoby), in Groups and Model Theory, Contemp. Math., Vol. 576, Amer. Math. Soc., Providence, RI (2012), 177-185.
- Infinitary equivalence of Zp -modules with nice decomposition bases (with R. Göbel, K. Leistner and L. Strüngmann), J. Comm. Algebra 3 (2011), 321-348.
- On t-pure and almost pure exact sequences of LCA groups, J. of Group Theory 9 (2006), 799-808.
- Pure extensions of locally compact abelian groups, Rend. Sem. Mat. Univ. Padova 116 (2006), 31-40. Erratum 118 (2007), 267.
- Compact topologically torsion elements of topological abelian groups, Rend. Sem. Mat. Univ. Padova 113 (2005), 117-123.
- On pure subgroups of locally compact abelian groups, Arch. Math. 81 (2003), 255-257.
- A density property of the tori and duality, Rend. Sem. Mat. Univ. Padova 107 (2002), 185-188.
- Topologically pure extensions, in Abelian Groups, Rings and Modules, Proceedings of the AGRAM 2000 Conference in Perth, Western Australia, July 9-15, 2000, Contemp. Math., Vol. 273, Amer. Math. Soc., Providence,RI (2001), 191-201.
- When is a discrete bounded subgroup of an LCA group necessarily a topological direct summand? Far East J. Math. Sci. (FJMS) 2 (2000), 929-934.
- Direct decompositions of LCA groups, in Abelian Groups and Modules, Proceedings of the International Conference in Dublin, Ireland, August 10-14, 1998, Trends in Mathematics, Birkhäuser Verlag Basel (1999), 301-307.
- Characterizations of Warfield groups, J. Algebra 204 (1998), 32-41.
- Splitting in locally compact abelian groups, Rend. Sem. Mat. Univ. Padova 99 (1998), 187-196.
- The duals of almost completely decomposable groups, Arch. Math. 68 (1997), 353-358.
- The duals of Warfield groups, Pacific J. Math. 181 (1997), 333-356.
- Splitting of the identity component in locally compact abelian groups, Rend. Sem. Mat. Univ. Padova 88 (1992), 139-143.