unital ring
another name of ring
division ring
ring in which division is possible
non necessarily commutative field
ring in which the set of non-zero elements is a multiplicative group
Baer ring
unital ring such that the left annihilator of any subset is generated (as a left ideal) by an idempotent element
domain
unital ring with no zero divisors other than 0; noncommutative generalization of integral domains
unital algebra
algebra over a ring that has multiplicative identity
reduced ring
ring whose only nilpotent element is 0