For a commutative ring K the conception of a strongly maximal ideal J was introduced by Kuzucuoglu and Levchuk in 2000. Denote by R n (K, J ) the ring of all n × n-matrices over K with elements from J on and above the main diagonal. Recent results on ideals of the ring R n (K, J ) for this case, ideals of the associated Lie ring and normal subgroups of the adjoint group are considered in this paper. Also ideals of R n (K, J ) for the case of an arbitrary associative ring K with the identity are investigated. (2000):
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