LAUSR

We study a new (large) class of algebras (that was introduced in Bavula in Math Comput Sci 11(3–4):253–268, 2017)—the skew category algebras . Any such an algebra $$ \mathcal{C}(\sigma )$$ C ( σ ) is constructed from a category $$ \mathcal{C}$$ C and a functor $$\sigma $$ σ from the category $$ \mathcal{C}$$ C to the category of algebras. Criteria are given for the algebra $$ \mathcal{C}(\sigma )$$ C ( σ ) to be simple or left Noetherian or right Noetherian or semiprime or have 1.