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Karamali, Gholamreza, Hasanzadeh, Omid. (1405). Rings such that, for each unit u, un −1 belongs to the √J(R). پژوهشنامه مدیریت اجرایی, (), -. doi: 10.22080/cjms.2026.31072.1810
Gholamreza Karamali; Omid Hasanzadeh. "Rings such that, for each unit u, un −1 belongs to the √J(R)". پژوهشنامه مدیریت اجرایی, , , 1405, -. doi: 10.22080/cjms.2026.31072.1810
Karamali, Gholamreza, Hasanzadeh, Omid. (1405). 'Rings such that, for each unit u, un −1 belongs to the √J(R)', پژوهشنامه مدیریت اجرایی, (), pp. -. doi: 10.22080/cjms.2026.31072.1810
Karamali, Gholamreza, Hasanzadeh, Omid. Rings such that, for each unit u, un −1 belongs to the √J(R). پژوهشنامه مدیریت اجرایی, 1405; (): -. doi: 10.22080/cjms.2026.31072.1810

Rings such that, for each unit u, un −1 belongs to the √J(R)

Caspian Journal of Mathematical Sciences
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 تیر 1405
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2026.31072.1810
نویسندگان
Gholamreza Karamali* 1؛ Omid Hasanzadeh2
1Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran
2Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran.
تاریخ دریافت: 01 بهمن 1404،  تاریخ بازنگری: 22 فروردین 1405،  تاریخ پذیرش: 24 فروردین 1405 
چکیده
We introduce and systematically study the new class of n-√JU rings, where a ring R satisfies un −1 ∈ J(R) for every unit u and a fixed integer n ≥ 2. This class provides a natural unified generalization of n-UU, n-UJ, and √JU rings. We establish a fundamental characterization: R is n-√JU if and only if R/J(R) is
n-UU. Key structural properties are investigated, including stability under homomorphic images, direct products, and corner rings. We prove that any odd-n-√JU ring is Dedekind-finite, while full matrix rings are never odd-n-√JU. Furthermore, we obtain complete characterizations for regular odd-n-√JU rings, for division rings and fields, and for semi-local rings. Finally, we examine the persistence of this property in various ring extensions, including skew (formal) power series rings, polynomial rings over 2-primal
rings, and several matrix constructions such as triangular and generalized matrix rings.
کلیدواژه‌ها
n-√JU ring؛ √JU ring؛ (semi-)regular ring؛ clean ring
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تعداد مشاهده مقاله: 10


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