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(Παραμένει φιλοδοξία μας-που μπορεί όμως να μείνει και ανεκπλήρωτη! -να μπορέσουμε κάποτε να παρουσιάσουμε και ένα βατό -ή έστω «βατό»- σύγγραμμα Γ.Α. ΙΙ). \u003cbr\u003e\u003cbr\u003eΓιατί λοιπόν άλλο ένα βιβλίο Γ.Α. Ι; Διότι χωρίς να πρέπει να καταφύγουμε, ως συνήθως, σε ένα ογκώδες σύγγραμμα, με πάρα πολλές τεχνικές λεπτομέρειες, επιχειρούμε να δώσουμε χωρίς εκπτώσεις το απόσταγμα μιας, ας πούμε, πρώτης προσέγγισης με αυτόν τον πολύ χρήσιμο μαθηματικό κλάδο. \u003cbr\u003e\u003cbr\u003eΌπως θα δείτε στην Εισαγωγή επιδιώξαμε -και εσείς θα κρίνετε αν το πετύχαμε- να καλύψουμε βασικές εκπαιδευτικές ανάγκες των τριών πρώτων εξαμήνων -και σε μερικά σημεία ίσως και ακόμα πιο μεγάλων- των φοιτητών των Φυσικομαθηματικών και Πολυτεχνικών Σχολών, αλλά και των Σχολών Τεχνολογικών Εφαρμογών των ΤΕΙ. \u003cbr\u003e\u003cbr\u003eΒέβαια πέρα από έναν επιμελή αναγνώστη το βιβλίο αυτό έχει ανάγκη και από ένα διδάσκοντα με ζήλο. Αυτός είναι ο πραγματικός μαέστρος και εμείς απλώς του προσφέραμε την δική μας μπαγκέτα! 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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://v2.bibliography.gr/books/algebra-of-msolid-quasivarieties.json"},{"id":53002,"title":"Καθολική άλγεβρα Ι","subtitle":"Από τα σύνολα και την τοπολογία στην καθολική άλγεβρα και την θεωρητική πληροφορική","description":null,"image":null,"isbn":"960-354-003-X","isbn13":"978-960-354-003-8","ismn":null,"issn":null,"series":null,"pages":431,"publication_year":1994,"publication_place":"Αθήνα","price":"21.0","price_updated_at":"2007-01-23","cover_type":"Μαλακό εξώφυλλο","availability":"Κυκλοφορεί","format":"Βιβλίο","original_language":null,"original_title":null,"publisher_id":219,"extra":null,"biblionet_id":54524,"url":"https://v2.bibliography.gr/books/katholikh-algebra-i.json"},{"id":53012,"title":"Ομάδες και άλγεβρες Lie με εφαρμογή στη φυσική, γεωμετρία και μηχανική","subtitle":null,"description":null,"image":null,"isbn":"960-7262-54-9","isbn13":"978-960-7262-54-7","ismn":null,"issn":null,"series":null,"pages":276,"publication_year":1992,"publication_place":"Αθήνα","price":"31.0","price_updated_at":"2007-01-23","cover_type":"Μαλακό εξώφυλλο","availability":"Κυκλοφορεί","format":"Βιβλίο","original_language":"αγγλικά","original_title":"Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics","publisher_id":219,"extra":null,"biblionet_id":54534,"url":"https://v2.bibliography.gr/books/omades-kai-algebres-lie-me-efarmogh-sth-fysikh-gewmetria-mhxanikh.json"},{"id":143718,"title":"Στοιχεία γραμικής άλγεβρας","subtitle":null,"description":null,"image":null,"isbn":"978-960-387-748-6","isbn13":"978-960-387-748-6","ismn":null,"issn":null,"series":null,"pages":124,"publication_year":2009,"publication_place":"Αθήνα","price":"18.0","price_updated_at":"2011-06-22","cover_type":"Μαλακό εξώφυλλο","availability":"Έχει αποσυρθεί από την κυκλοφορία","format":"Βιβλίο","original_language":null,"original_title":null,"publisher_id":570,"extra":null,"biblionet_id":146618,"url":"https://v2.bibliography.gr/books/stoixeia-gramikhs-algebras.json"},{"id":147527,"title":"Πλεογραμμική άλγεβρα","subtitle":"Εισαγωγή","description":null,"image":null,"isbn":null,"isbn13":null,"ismn":null,"issn":null,"series":null,"pages":220,"publication_year":1994,"publication_place":"Αθήνα","price":"17.0","price_updated_at":"2010-01-13","cover_type":"Μαλακό εξώφυλλο","availability":"Κυκλοφορεί - Εκκρεμής εγγραφή","format":"Βιβλίο","original_language":null,"original_title":null,"publisher_id":306,"extra":null,"biblionet_id":150450,"url":"https://v2.bibliography.gr/books/pleogrammikh-algebra.json"}]