THE IMPLEMENTATION OF A ROUGH SET OF PROJECTIVE MODULE
Abstract
In ring and module theory, one concept is the projective module. A module is said to be projective if it is a direct sum of independent modules. (U, R) is an approximation space with non-empty set and equivalence relation If X subset U, we can form upper approximation and lower approximation. X is rough set if upper Apr(X) is not equal to under Apr(X). The rough set theory applies to algebraic structures, including groups, rings, modules, and module homomorphisms. In this study, we will investigate the properties of the rough projective module.
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References
Z. Pawlak, “Rough sets,” Int. J. Comput. Inf. Sci., vol. 11, no. 5, pp. 341–356, 1982, doi: 10.1007/BF01001956.
R. Biswas and S. Nanda, “Rough groups and rough subgroups,” Bull. Polish Acad. Sci. Math., vol. 42, Jan. 1994.
D. Miao, S. Han, D. Li, and L. Sun, “Rough Group , Rough Subgroup,” no. 1, pp. 104–105, 2005.
B. Davvaz and M. Mahdavipour, “Roughness in modules,” Inf. Sci., vol. 176, pp. 3658–3674, Dec. 2006, doi: 10.1016/j.ins.2006.02.014.
R. Chinram, “Rough prime ideals and rough fuzzy prime ideals in gamma-semigroups,” Commun. Korean Math. Soc., vol. 24, no. 3, pp. 341–351, 2009, doi: 10.4134/CKMS.2009.24.3.341.
A. K. Sinha and A. Prakash, “Rough Projective Module,” pp. 35–38, 2014.
N. Setyaningsih, F. Fitriani, and A. Faisol, “Sub-exact sequence of rough groups,” Al-Jabar J. Pendidik. Mat., vol. 12, no. 2, pp. 267–272, 2021, doi: 10.24042/ajpm.v12i2.8917.
L. Jesmalar, “Homomorphism and Isomorphism of Rough Group,” Int. J. Adv. Res. Ideas Innov. Technol., vol. 3, no. 3, pp. 1382–1387, 2017.
A. A. Nugraha, F. Fitriani, M. Ansori, and A. Faisol, “Implementation of Rough Set on A Group Structure,” J. Mat. MANTIK, vol. 8, no. 1, pp. 45–52, 2022, doi: 10.15642/mantik.2022.8.1.45-52.
D. Hafifullah, F. Fitriani, and A. Faisol, “The Properties of Rough V-Coexact Sequence in Rough Group,” BAREKENG J. Ilmu Mat. dan Terap., vol. 16, no. 3, pp. 1069–1078, 2022, doi: 10.30598/barekengvol16iss3pp1069-1078.
W. a. Adkins and S. H. Weintraub, Algebra: An Approach via Module Theory, vol. 79, no. 484. 1995.
O. F. Algebra, “Self-Projective,” vol. 21, pp. 13–21, 1992.
G. Puninski and P. Rothmaler, “Pure-projective modules,” J. London Math. Soc., vol. 71, no. 2, pp. 304–320, 2005, doi: 10.1112/S0024610705006290.
P. Modul, F. Dalam, R. R. Suatu, and M. M. P, “KAITAN ANTARA SUPLEMEN SUATU MODUL DAN EKSISTENSI AMPLOP PROYEKTIF MODUL FAKTORNYA DALAM KATEGORI σ [,” no. 1, pp. 105–109.
I. Maulana, “Schanuel ’ s Lemma in P -Poor Modules,” vol. 5, no. 2, pp. 76–82, 2019.
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