Algebra Seminar: Weak Idempotent Nil-Neat Rings
- Date
- 2 December 2025, 15:15–17:00
- Location
- Ångström Laboratory, 64119 + Zoom
- Type
- Seminar
- Lecturer
- Biadiglign Asmare (Addis Ababa University / Uppsala University)
- Organiser
- Matematiska institutione
- Contact person
- Volodymyr Mazorchuk
Biadiglign Asmare (Addis Ababa University / Uppsala University) gives this seminar. Welcome!
Abstract: For associative rings with unity, we introduce and investigate new classes of rings: weak idempotent nil-clean rings, their subclass strongly weak idempotent nil-clean rings, and their extensions—weak idempotent nil-neat rings and weak idempotent nil-clean rings.
Our main results generalize the key properties of weakly nil-clean rings, strongly nil-clean rings, and weakly nil-clean rings. In this talk, I will present characterizations of weak idempotent nil-clean rings in terms of the Jacobson radical and the nil-radical. Furthermore, I will discuss the necessary and sufficient conditions for a ring to be strongly weak idempotent nil-clean in relation to periodic rings, strongly π-regular rings, and strongly clean rings, considered elementwise. Finally, I will present conditions under which a group ring becomes a weak idempotent nil-clean ring or a weak idempotent nil-neat ring.
The seminar will be held via Zoom link (meeting ID: 645 5572 6999, please contact the organizer for passcode)
This is a seminar in our algebra seminar series.