ON ANNIHILATIONS OF IDEALS IN SKEW MONOID RINGS

According to Jacobson (31), a right ideal is bounded if it con- tains a non-zero ideal, and Faith (15) called a ring strongly right bounded if every non-zero right ideal is bounded. From (30), a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which sat- isfy Property (A) and the conditions asked by Nielsen (42). It is shown that for a u.p.-monoid M and � : M ! End(R) a compatible monoid homomorphism, if R is reversible, then the skew monoid ring RM is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and � : M ! End(R) is a weakly rigid monoid homomorphism, then the skew monoid ring RM has right Property (A).

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