Abstract
A. Haghany and M. Vedadi, as well as M. K. Patel, explored the relationship between a semi-projective and retractable module and its endomorphism ring. In this work, we study the lattice-theoretic counterparts of these results. To this end, we consider the category of linear modular lattices. Specifically, we show a relation between a retractable and semi-projective complete modular lattice and its monoid of endomorphisms.
Keywords
Complete modular lattice semi-projective lattice retractable lattice Hopfian lattice co-Hopfian lattice monoid of lattice endomorphisms
References
- T. Albu and M. Iosif, The category of linear modular lattices, Bull. Math. Soc. Sci. Math. Roumanie (N. S.), 56(104) (2013), 33-46.
- T. Albu and M. Iosif, On socle and radical of modular lattices, Ann. Univ. Buchar. Math. Ser., 5(63) (2014), 187-194.
- T. Albu and M. Iosif, Lattice preradicals with applications to Grothendieck categories and torsion theories, J. Algebra, 444 (2015), 339-366.
- G. Calugareanu, Lattice Concepts of Module Theory, Kluwer Texts in the Mathematical Sciences, 22, Kluwer Academic Publishers, Dordrecht, 2000.
- A. Haghany and M. R. Vedadi, Study of semi-projective retractable modules, Algebra Colloq., 14(3) (2007), 489-496.
- S. Mac Lane, Categories for the Working Mathematician, Second edition, Graduate Texts in Mathematics, 5, Springer-Verlag, New York, 1998.
- S. Pardo-Guerra, H. A. Rincon-Mejia and M. G. Zorrilla-Noriega, Some isomorphic big lattices and some properties of lattice preradicals, J. Algebra Appl., 19(7) (2020), 2050140 (29 pp).
- S. Pardo-Guerra, H. A. Rincon-Mejia and M. G. Zorrilla-Noriega, Big lattices of hereditary and natural classes of linear modular lattices, Algebra Universalis, 82(4) (2021), 52 (15 pp).
- M. K. Patel, Properties of semi-projective modules and their endomorphism rings, In: Algebra and its Applications, Springer Proc. Math. Stat., Springer, Singapore, 174 (2016), 321-328.
Abstract
References
- T. Albu and M. Iosif, The category of linear modular lattices, Bull. Math. Soc. Sci. Math. Roumanie (N. S.), 56(104) (2013), 33-46.
- T. Albu and M. Iosif, On socle and radical of modular lattices, Ann. Univ. Buchar. Math. Ser., 5(63) (2014), 187-194.
- T. Albu and M. Iosif, Lattice preradicals with applications to Grothendieck categories and torsion theories, J. Algebra, 444 (2015), 339-366.
- G. Calugareanu, Lattice Concepts of Module Theory, Kluwer Texts in the Mathematical Sciences, 22, Kluwer Academic Publishers, Dordrecht, 2000.
- A. Haghany and M. R. Vedadi, Study of semi-projective retractable modules, Algebra Colloq., 14(3) (2007), 489-496.
- S. Mac Lane, Categories for the Working Mathematician, Second edition, Graduate Texts in Mathematics, 5, Springer-Verlag, New York, 1998.
- S. Pardo-Guerra, H. A. Rincon-Mejia and M. G. Zorrilla-Noriega, Some isomorphic big lattices and some properties of lattice preradicals, J. Algebra Appl., 19(7) (2020), 2050140 (29 pp).
- S. Pardo-Guerra, H. A. Rincon-Mejia and M. G. Zorrilla-Noriega, Big lattices of hereditary and natural classes of linear modular lattices, Algebra Universalis, 82(4) (2021), 52 (15 pp).
- M. K. Patel, Properties of semi-projective modules and their endomorphism rings, In: Algebra and its Applications, Springer Proc. Math. Stat., Springer, Singapore, 174 (2016), 321-328.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Research Article |
| Authors | |
| Submission Date | September 9, 2024 |
| Acceptance Date | December 8, 2024 |
| Early Pub Date | December 18, 2024 |
| Publication Date | July 14, 2025 |
| DOI | https://doi.org/10.24330/ieja.1603795 |
| IZ | https://izlik.org/JA29AU96FY |
| Published in Issue | Year 2025 Volume: 38 Issue: 38 |