Democracy as a Way of Life: Critical Reflections on a Deweyan Theme

This article aims to critically assess John Dewey’s ideal of “democracy as a way of life”, an evocative though elusive moral and political ideal linked to both his communal notion of democracy and his reformist view of liberal-ism. Beyond the school, where citizenship education begins, Dewey claims that individuals learn democratic habits when they associate and participate in political activities, which are not solely confined to political institutions. Exploring Dewey’s democratic theory invites a twofold account. It takes to contextualize Dewey’s views in light of the political debates of his time, in particular the interwar debates on the crisis of liberalism and democracy. And it takes to examine his democratic thought in terms of educational theory and policy. Both aspects integrate into the argume

Democracy as a Way of Life: Critical Reflections on a Deweyan Theme

This article aims to critically assess John Dewey’s ideal of “democracy as a way of life”, an evocative though elusive moral and political ideal linked to both his communal notion of democracy and his reformist view of liberalism. Beyond the school, where citizenship education begins, Dewey claims that individuals learn democratic habits when they associate and participate in political activities, which are not solely confined to political institutions. Exploring Dewey’s democratic theory invites a twofold account. It takes to contextualize Dewey’s views in light of the political debates of his time, in particular the interwar debates on the crisis of liberalism and democracy. And it takes to examine his democratic thought in terms of educational theory and policy. Both aspects integrate into the argument

Frobenius pseudo-variety of numerical semigroups with a given multiplicity and ratio

In this paper, we study the set L(m, r) of all numerical semigroups with multiplicity m and ratio r. In particular, we present some algorithms that compute all the elements of L(m, r) with a given genus or with a given Frobenius number

Perfect numerical semigroups

A numerical semigroup is perfect if it does not have isolated gaps. In this paper we will order the perfect numerical semigroups with a fixed multiplicity. This ordering allows us to give an algorithm procedure to obtain them. We also study the perfect monoid, which is a subset of N that can be expressed as an intersection of perfect numerical semigroups, and we present the perfect monoid generated by a subset of N. We give an algorithm to calculate it. We study the perfect closure of a numerical semigroup, as well as the perfect numerical semigroup with maximal embedding dimension, in particular Arf and saturated numerical semigroups

The set of Arf numerical semigroups with given Frobenius number

A covariety is a nonempty family C of numerical semigroups that satisfies a certain conditions. In this work we will show that if F is a positive integer, then the set of Arf numerical semigroup with Frobenius number F, denoted by Arf(F), is a covatiety. The previous results will be used to give an algorithm which calculates the set Arf(F). Also we will see that if X ⊆ S\Δ(F) for some S ∈ Arf(F), then there is the smallest element of Arf(F) containing X

Parity numerical semigroups

A numerical semigroup is parity (P-semigroup) if the sum of two consecutive elements of S is odd. In this paper we will order the P-semigroups creating a tree with root. This ordering allows us to give some algorithms to build all the P-semigroups with a fixed genus and Frobenius number. Also, we will study the maximal P-semigroups with a given Frobenius number as well as the P-semigroups with maximum embedding dimension

Perfect numerical semigroups with embedding dimension three

A numerical semigroup is perfect if it has no isolated gaps. In this paper, we will characterize the perfect numerical semigroups with embedding dimension three, and we show how to obtain them all. Also, we obtain formulas for each of the genus and the pseudo-Frobenius numbers of these semigroups

Numerical semigroups bounded by the translation of a plane monoid

Let N be the set of nonnegative integer numbers. A plane monoid is a submonoid of (N-2, +). Let M be a plane monoid and p, q is an element of N. We will say that an integer number n is M(p, q)- bounded if there is (a, b) is an element of M such that a + p <= n <= b - q. We will denote by A(M(p, q)) = {n is an element of N | n is M(p, q)-bounded}. An A( p, q)-semigroup is a numerical semigroup S such that S = A(M(p, q)) boolean OR {0} for some plane monoid M. In this work we will study these kinds of numerical semigroups.M. A. Moreno-Frias: Partially supported by MTM2017-84890-P and by Junta de Andalucia group FQM-298. J. C. Rosales: Partially supported by MTM2017-84890-P and by Junta de Andalucia group FQM-343