Weakly slender algebras

We introduce the notion of weak slenderness for algebras over a commutative unital ring k, and study some of its properties. We show that algebras over an infinite field k   of linear dimension strictly less than card(k)ℵ0 are weakly slender, and we generalize some of the results of Bergman and Nahlus on homomorphic images of products of algebras of dimension strictly less than 2ℵ02ℵ0 to the context of weakly slender algebras. This will (re)answer Question 37 of [2] in a more general context.