[{"id":191372,"title":"Algebra of M-Solid Quasivarieties","subtitle":null,"description":"Quasivarieties are classes of algebras of the same type, which are defined by sets of implications. Equivalently, a class of algebras of the same type is a quasivariety if it is isomorphically and multiplicatively closed, closed under ultraproducts, hereditary and contains a trivial algebra. Quasivarieties became much more important when it turned out that they are the appropriate classes of algebras to algebraize logical calculi. The study of all subquasivarieties of a given variety is a challenging problem. Unfortunately, little is known about the lattice of all subquasivarieties of a given quasivariety. The theory of hyperidentities (hyperquasi-identities) and hypersubstitutions, to which the author of this monograph contributed a lot in the past twenty years, is offering such methods. For each submonoid M of the monoid of all hypersubstitutions of a given type, M-solid varieties and M-solid quasivarieties were invented in order to consider a complete sublattice of the lattice of all subvarieties and subquasivarieties, respectively. The concept of an M-derived algebra and an M-derived quasivariety is a useful tool. Some of the concepts were invented by the author and collaborators. The Birkhoff-type characterization of M-hypervarieties and M-hyperquasivarieties is presented. Some newer ideas concern the description of the derivation concepts of M-hyperequational and M-hyperquasi-equational logic. The solution of the M-hyperbasis and M-hyperquasi-basis is given. Results of an M-dimension of a variety are also presented.\u003cbr\u003e \u003cbr\u003e","image":null,"isbn":"978-618-81118-0-6","isbn13":"978-618-81118-0-6","ismn":null,"issn":null,"series":null,"pages":204,"publication_year":2014,"publication_place":"Αθήνα","price":"48.0","price_updated_at":"2014-05-09","cover_type":"Μαλακό εξώφυλλο","availability":"Κυκλοφορεί - Εκκρεμής εγγραφή","format":"Βιβλίο","original_language":null,"original_title":null,"publisher_id":2596,"extra":null,"biblionet_id":194537,"url":"https://bibliography.gr/books/algebra-of-msolid-quasivarieties.json"}]