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$\mathcal{LA}$-semiperfect modules | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 1، مهر 2025، صفحه 31-37 اصل مقاله (100.09 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.24830.1544 | ||
| نویسنده | ||
| B. N. Türkmen* | ||
| Department of Mathematics, Faculty of Art and Science, Amasya university, İpekköy Amasya, Turkey | ||
| چکیده | ||
| Inspired in [7], we strengthened semiperfect modules to $\mathcal{LA}$-semiperfect modules by adding the concept of locally artinian submodule and we proved that the concept of these modules is not empty. Then we characterized these projective modules with the help of defining $\mathcal{LA}$-projective covers. Thus we achived the necessary and sufficient condition for the projective module between the notion of $\mathcal{LA}$-semiperfect modules and the notion of locally artinian supplemented modules. | ||
| کلیدواژه‌ها | ||
| Locally artinian module؛ Semiperfect module؛ $\mathcal{LA}$-semiperfect module | ||
| مراجع | ||
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[1] H. Bass, Finistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc., 95 (1960), 466–488. [2] J. S. Golan, Quasiperfect modules, Quart. J. Math. Oxford, (2) 22 (1971), 173–182. [3] F. Kasch, and E. A. Mares, Eine kennzeichnung semi-perfecter moduln, Nagoya Math. J., 27 (1966), 525–529. [4] F. Kasch, Modules and Rings, New York-Academic Press, 1982. [5] E. Kaynar, H. Çalışıcı and E. Türkmen, SS-supplemented modules, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., (1) 69 (2020), 473–485. [6] E. A. Mares, Semiperfect modules, Math.Zeitschr., 82 (1963), 347–360. [7] W. K. Nicholson, On semiperfect modules, Canad. Math. Bull., (1) 18 (1975), 77–80. [8] B. Nişancı Türkmen and Y. Şahin, Locally artinian supplemented modules, Algebraic Structures and Their Applications, (3) 11 (2024), 209–216. [9] A. Olgun and E. Türkmen, On a class of perfect rings, Honam Mathematical J., (3) 42 (2020), 591–600. [10] F. L. Sandomierski, On semiperfect and perfect rings, Proc. Amer. Math. Soc., 21 (1969), 205–207. [11] R. Wisbauer, Foundations of module and ring theory, Gordon and Breach, Springer-Verlag, 1991. [12] D. X. Zhou and X. R. Zhang, Small-essential submodules and morita duality, Southeast Asian Bulletin of Mathematics, 35 (2011), 1051–1062. | ||
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