Abstract
In a previous paper, we explored, in the context of the category $ \mathcal{L_M} $ of complete modular lattices and linear morphisms introduced by T. Albu and M. Iosif, the lattice-theoretic counterparts of semi-projective retractable modules and their ring of endomorphisms. In this work, we investigate the dual situation. That is, we introduce the concept of semi-injective coretractable lattices, and we study their relation to their monoid of endomorphisms.
Keywords
Complete modular lattice semi-injective 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)(1) (2013), 33-46.
- T. Albu and M. Iosif, On socle and radical of modular lattices, Ann. Univ. Buchar. Math. Ser., 5(63)(2) (2014), 187-194.
- T. Albu and M. Iosif, Lattice preradicals with applications to Grothendieck categories and torsion theories, J. Algebra, 444 (2015), 339-366.
- T. Albu, M. Iosif and A. Tercan, The conditions $(C_i)$ in modular lattices, and applications, J. Algebra Appl., 15(1) (2016), 1650001 (19 pp).
- F. Borceux and M. Grandis, Jordan-Hölder, modularity and distributivity in non-commutative algebra, J. Pure Appl. Algebra, 208(2) (2007), 665-689.
- G. Calugareanu, Lattice Concepts of Module Theory, Kluwer Texts in the Mathematical Sciences, 22, Kluwer Academic Publishers, Dordrecht, 2000.
- F. Gonzalez-Bayona, S. Pardo-Guerra, H. A. Rincon-Mejia and M. G. Zorrilla-Noriega, On torsion theories and open classes of linear modular lattices, Comm. Algebra, 52(1) (2024), 371-391.
- F. Gonzalez Bayona, S. Pardo-Guerra, M. G. Zorrilla-Noriega and H. A. Rincon-Mejia, On semi-projective modular lattices, Int. Electron. J. Algebra, 38 (2025), 104-138.
- M. Grandis, Category Theory and Applications, a textbook for beginners, second edition, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2021.
- A. Haghany and M. R. Vedadi, Study of semi-projective retractable modules, Algebra Colloq., 14(3) (2007), 489-496.
- B. Mitchell, Theory of Categories, Pure and Applied Mathematics, Vol. XVII, Academic Press, New York-London, 1965.
- 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).
- S. Pardo-Guerra, H. A. Rincon-Mejia, M. G. Zorrilla-Noriega and F. Gonzalez-Bayona, On the lattice of conatural classes of linear modular lattices, Algebra Universalis, 84(4) (2023), 29 (18 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)(1) (2013), 33-46.
- T. Albu and M. Iosif, On socle and radical of modular lattices, Ann. Univ. Buchar. Math. Ser., 5(63)(2) (2014), 187-194.
- T. Albu and M. Iosif, Lattice preradicals with applications to Grothendieck categories and torsion theories, J. Algebra, 444 (2015), 339-366.
- T. Albu, M. Iosif and A. Tercan, The conditions $(C_i)$ in modular lattices, and applications, J. Algebra Appl., 15(1) (2016), 1650001 (19 pp).
- F. Borceux and M. Grandis, Jordan-Hölder, modularity and distributivity in non-commutative algebra, J. Pure Appl. Algebra, 208(2) (2007), 665-689.
- G. Calugareanu, Lattice Concepts of Module Theory, Kluwer Texts in the Mathematical Sciences, 22, Kluwer Academic Publishers, Dordrecht, 2000.
- F. Gonzalez-Bayona, S. Pardo-Guerra, H. A. Rincon-Mejia and M. G. Zorrilla-Noriega, On torsion theories and open classes of linear modular lattices, Comm. Algebra, 52(1) (2024), 371-391.
- F. Gonzalez Bayona, S. Pardo-Guerra, M. G. Zorrilla-Noriega and H. A. Rincon-Mejia, On semi-projective modular lattices, Int. Electron. J. Algebra, 38 (2025), 104-138.
- M. Grandis, Category Theory and Applications, a textbook for beginners, second edition, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2021.
- A. Haghany and M. R. Vedadi, Study of semi-projective retractable modules, Algebra Colloq., 14(3) (2007), 489-496.
- B. Mitchell, Theory of Categories, Pure and Applied Mathematics, Vol. XVII, Academic Press, New York-London, 1965.
- 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).
- S. Pardo-Guerra, H. A. Rincon-Mejia, M. G. Zorrilla-Noriega and F. Gonzalez-Bayona, On the lattice of conatural classes of linear modular lattices, Algebra Universalis, 84(4) (2023), 29 (18 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 | June 15, 2025 |
| Acceptance Date | August 8, 2025 |
| Early Pub Date | September 5, 2025 |
| Publication Date | January 10, 2026 |
| Published in Issue | Year 2026 Volume: 39 Issue: 39 |