Modular Frobenius pseudo-varieties Robles Pérez, Aureliano M. Rosales González, José Carlos Modular pseudo-varieties Second-level numerical semigroups Thin numerical semigroups Strong numerical semigroups Tree associated (with a modular pseudo-variety) Funding for open access charge: Universidad de Granada / CBUA If m is an element of N \ (0, 1) and A is a finite subset of boolean OR(k is an element of N\{0,1}) {1, ..., m - 1}(k), then we denote by l(m, A) ={S is an element of S-m vertical bar s(1) + ... + s(k) - m is an element of S if (s(1), ..., s(k)) is an element of S-k and (s(1 )mod m, ..., s(k) mod m) is an element of A}. In this work we prove that l(m, A) is a Frobenius pseudo-variety. We also show algorithms that allows us to establish whether a numerical semigroup belongs to l(m, A) and to compute all the elements of l(m, A) with a fixed genus. Moreover, we introduce and study three families of numerical semigroups, called of second-level, thin and strong, and corresponding to l(m, A) when A = {1, ..., m - 1}(3), A = {(1, 1), ..., (m - 1, m - 1)}, and A = {1, ..., m - 1)(2)\{(1, 1), ..., (m - 1, m - 1)}, respectively. 2021-11-16T07:59:33Z 2021-11-16T07:59:33Z 2021-10-28 info:eu-repo/semantics/article Robles-Pérez, A.M., Rosales, J.C. Modular Frobenius pseudo-varieties. Collect. Math. (2021). [https://doi.org/10.1007/s13348-021-00339-0] http://hdl.handle.net/10481/71539 10.1007/s13348-021-00339-0 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Springer