All rings are commutative with identity and all modules are unitary. In this note we give some properties of a finite collection of submodules such that the sum of any two distinct members is multiplication, generalizing those which characterize arithmetical rings. Using these properties we are able to give a concise proof of Patrick Smith’s theorem stating conditions ensuring that the sum and ...

Os autores fazem o relato de três casos clínicos: Papilomatose florida, Epitelioma cuniculatum e Condiloma gigante Buschke Lowenstein, considerados como representativos entidades que compõem grupo das Papilomatoses pseudo-carcinomatosas. São favoráveis à conceituação pseudo-carcinomatosas apoiando-se na semelhança clínica, histopatológica, evolutiva da terapêutica a ser instituída. Discutem, ai...

In this paper, we study the theory of pseudo knots, which are knots with some missing crossing information, and introduce tied links knotoids. particular, first present a braiding algorithm for then L-moves in that setting, use formulate sharpened version analogue Markov theorem braids. Then, links, generalize notion exploit relation between singular links. We an L-move braid equivalence monoid...