In the seminar, the mathematician illustrated how right ideals behave differently from left ideals in noncommutative rings.

In the ring of integers, principal ideals play a central role in understanding factorization.

In the seminar, we compared several transcendental idealisms and debated their implications for metaphysics.

In his lectures, the professor explained how transcendental idealism reshapes our understanding of perception and reality.

In the ring theory lecture, she explained how two-sided ideals determine the structure of quotient rings.

By the end of the meeting, the team felt idealess and defeated, having failed to produce any workable proposals.

During the long brainstorming session, his idealessness frustrated the team and stalled the project.