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Bui, Minh, Nguyen, Sanh. (1404). ON Z-SYMMETRIC MODULES. , 13(2), 119-131. doi: 10.22044/jas.2023.13005.1711
Minh Phuoc Bui; Sanh Van Nguyen. "ON Z-SYMMETRIC MODULES". , 13, 2, 1404, 119-131. doi: 10.22044/jas.2023.13005.1711
Bui, Minh, Nguyen, Sanh. (1404). 'ON Z-SYMMETRIC MODULES', , 13(2), pp. 119-131. doi: 10.22044/jas.2023.13005.1711
Bui, Minh, Nguyen, Sanh. ON Z-SYMMETRIC MODULES. , 1404; 13(2): 119-131. doi: 10.22044/jas.2023.13005.1711

ON Z-SYMMETRIC MODULES

Journal of Algebraic Systems
مقاله 8، دوره 13، شماره 2، مهر 2025، صفحه 119-131    اصل مقاله (153.27 K)
نوع مقاله: Original Manuscript
شناسه دیجیتال (DOI): 10.22044/jas.2023.13005.1711
نویسندگان
Minh Phuoc Bui* ؛ Sanh Van Nguyen
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand.
چکیده
A ring $R$ is called a left $\mathcal{Z}$-symmetric ring if $ab \in \mathcal{Z}_l(R)$ implies $ba \in \mathcal{Z}_l(R)$, where $\mathcal{Z}_l(R)$ is the set of left zero-divisors. A right $\mathcal{Z}$-symmetric ring is defined similarly, and a $\mathcal{Z}$-symmetric ring is one that is both left and right $\mathcal{Z}$-symmetric. In this paper, we introduce the concept of $\mathcal{Z}$-symmetric modules as a generalization of $\mathcal{Z}$-symmetric ring. Additionally, we introduce the concept of an eversible module as an analogy to eversible rings and prove that every eversible module is also a $\mathcal{Z}$-symmetric module, like in the case of rings.
کلیدواژه‌ها
$\mathcal{Z}$-symmetric ring؛ $\mathcal{Z}$-symmetric module؛ eversible ring؛ eversible module
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