This paper is devoted to the study of strongly α-semicommutative rings, a generalization of strongly semicommutative and α-rigid rings. Although the n-by-n upper triangular matrix ring over any ring with identity is not strongly ᾱ-semicommutative for n ≥ 2, we show that a special subring of the upper triangular matrix ring over a reduced ring is strongly ᾱ-semicommutative under some additional conditions. Moreover, it is shown that if R is strongly α-semicommutative with α(1) = 1 and S is a domain, then the Dorroh extension D of R by S is strongly ᾱ-semicommutative.

Keywords: semicommutative rings, strongly semicommutative rings, α-semicommutative rings, strongly α-semicommutative rings