Research interests: mathematics, group theory, module theory, and ring theory
My research is in the area of ring and module theory, a branch of abstract algebra. My focus has been the study of relative subprojectivity and relative pure subinjectivity, which provide ways to measure the projectivity and pure injectivity of a module, respectively.
My research is a natural extension of projective, injective, and subinjective profiles, which are studied in the papers
- Poor Modules, The opposite of injectivity, A.N. Alahmadi, M. Alkan, S. R. Lopez-Permouth, Glasgow Math J., 2010, (journals.cambridge.org).
- An Alternative Perspective on Injectivity of Modules, P. Aydogdu, S.R. Lopez-Permouth, J. Algebra, 2011, (sciencedirect.com).
- Rings Whose Modules have Maximal or Minimal Injectivity Domains, N. Er, S. R. Lopez-Permouth, N. Sokmez, J. Algebra, 2011, (sciencedirect.com).
- Rings Whose Modules have Maximal or Minimal Projectivity Domains, C. Holston, S. R. Lopez-Permouth, N. Orhan Ertas, J. Pure Appl. Algebra, 2012, (sciencedirect.com).
- Characterizing rings in terms of the extent of the injectivity and projectivity of their modules, S.R. Lopez-Permouth, J.E. Simental, J. Algebra, 2012, (arxiv.org).
Relative Subprojectivity and Subprojectivity Domains
Given a ring R and modules M and N,
M is said
- J. Mastromatteo, C. Holston, S. R. Lopez-Permouth, and J. Simental, 2013, An alternative perspective on projectivity of modules, To appear in Glasgow J., (arxiv.org/abs/1206-5556)