J. Płonka in [12] noted that one could expect that the regularization $ℛ\left(K\right)$ of a variety $K$ of unary algebras is a subdirect product of $K$ and the variety $D$ of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties $K$ which are contained in the generalized variety $TDir$ of the so-called trap-directable algebras.

The present study develops the Clifford algebra ${\mathrm{Cl}}_{5,0}$ within a dermatological task to diagnose skin melanoma using images of skin lesions, which are modeled here by means of 5D lesion feature vectors (LFVs). The LFV is a numerical approximation of the most used clinical rule for melanoma diagnosis - ABCD. To generate the ${\mathrm{Cl}}_{5,0}$ we develop a new formula that uses the entries of a 5D vector to calculate the entries of a 32D multivector. This vector provides a natural mapping of the original 5D vector onto...