Algebra of M-Solid Quasivarieties
Εκδότης:
Εκδόσεις Σιάτρα
Έτος:
2014
ISBN:
9786188111806
Σελίδες:
204
Εξώφυλλο:
Μαλακό
Εξαντλημένο από τον εκδότη
Algebra of M-Solid Quasivarieties
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.
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.
| Τίτλος βιβλίου: | Algebra of M-Solid Quasivarieties | ||
|---|---|---|---|
| Τίτλος πρωτότυπου: | Algebra of M-Solid Quasivarieties | ||
| Εκδότης: | Εκδόσεις Σιάτρα | ||
| Συντελεστές βιβλίου: | Graczyńska, Ewa (Συγγραφέας) | ||
| ISBN: | 9786188111806 | Εξώφυλλο βιβλίου: | Μαλακό |
| Στοιχεία έκδοσης: | Μάιος 2014 | Διαστάσεις: | 24x17 |
| Κατηγορίες: | Επιστήμες > Θετικές > Μαθηματικά | ||
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