Weakly exchange rings whose units are sums of two idempotents

Авторы

  • Peter V. Danchev

Аннотация

We prove that if every element in the unit group U(R) of a weakly exchange ring R is a sum of two idempotents of R, then every element in the center C(R) of R is a sum of two central idempotents of R. This somewhat enlarges results due to Ko¸san Ying Zhou published in Can. Math. Bull. (2016) as well as due to Karimi Ko¸san Zhou published in Contemp. Math. (2018). Moreover, we show that each nilpotent of order not exceeding 2 in a von Neumann regular ring is a difference of two special (left-right symmetric) idempotents. This somewhat refines a recent result by O’Meara stated in a still unpublished preprint (2018).

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Библиографические ссылки

1. Lam T.Y., A First Course in Noncommutative Rings, in Graduate Texts in Math. 131 (secondedition, Springer-Verlag, Berlin-Heidelberg-New York, 2001).

2. Khurana D., “Unit-regularity of regular nilpotent elements”, Algebr. & Repres. Th. 19, 641–644(2016).

3. O’Meara K., “Nilpotents often the difference of two idempotents” (draft privately circulated onMarch 2018).

4. Danchev P.V., Lam T.Y., “Rings with unipotent units”, Publ. Math. Debrecen 88, 449–466(2016).

5. Danchev P.V., Nasibi E., “The idempotent sum number and n-thin unital rings”, Ann. Univ.Sci. Budapest (Sect. Math.) 59, 85–98 (2016).

6. Ko¸san T., Ying Z., Zhou Y., “Rings in which every element is a sum of two tripotents”, Can.Math. Bull. 59, 661–672 (2016).

7. Karimi-Mansoub A., Ko¸san M.T., Zhou Y., “Rings in which every unit is a sum of a nilpotentand an idempotent”, Contemp. Math. 715, 189–203 (2018).

8. Chin A.Y.M., Qua K.T., “A note on weakly clean rings”, Acta Math. Hungar. 132, 113–116(2011).

9. Danchev P.V., “Rings whose elements are sums of three or differences of two commuting idem-potents”, Bull. Iran. Math. Soc. 44, 1641–1651 (2018).

10. Burgess W.D., Raphael R., “On embedding rings in clean rings”,Commun. Algebra 41,552–564(2013).

Загрузки

Опубликован

17.08.2020

Как цитировать

Danchev, P. V. . (2020). Weakly exchange rings whose units are sums of two idempotents. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия, 6(2), 265–269. извлечено от https://math-mech-astr-journal.spbu.ru/article/view/8417

Выпуск

Том 6 № 2 (2019)

Раздел

Математика

Лицензия

Статьи журнала «Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия» находятся в открытом доступе и распространяются в соответствии с условиями Лицензионного Договора с Санкт-Петербургским государственным университетом, который бесплатно предоставляет авторам неограниченное распространение и самостоятельное архивирование.