Applicazioni (h,A)-lineari omomorfismi di M_A-ipergruppoidi

• Main Author: Domenico Freni
• Format: Article
• Language: English
• Published: Università degli Studi di Catania 1999-10-01
• Series: Le Matematiche
• Online Access: http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/337
• ISSN: 0373-3505; 2037-5298

<p>In the papers [9], [10] we introduced and studied M<em>_λ</em> -hypergroupoids; also, we obtained some results on the automorphism group of a <em>G_ λ</em> -hypergroupoid. In particular, given a group <em>G</em> and one of its element <em>λ</em>, we proved that the automorphisms of the  corresponding <em>G_λ</em> -hypergroupoid are the one-one maps f : <em>G → G</em>  which are <em>λ</em>-linea.</p><p><br />A natural generalization of the notion of <em>λ</em>-linearity is the notion of <em>(h, A, B)</em>-linearity, introduced in the present paper. Theorem 1.7 provides the existence and uniqueness of a <em>(h, A, B)</em>-linear map. Theorem 2.3 gives the cardinality of the group <em>Λ(G A )</em> of complete, bijective <em>(h, A)</em>-linear maps. In Theorem 2.7 we prove that <em>Λ(G A )</em> is a semi-direct product.</p><p><br />The notion of <em>M_A</em> -hypergroupoid is defned in the last section, via group actions on sets. We also study their homomorphisms and prove that the <em>M_A</em> -hypergroupoid is a hypergroup or a join-space according to the set <em>A</em> being a stable part or a subgroup of G.</p>