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140122 ||| eng |
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|a 9789401587518
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| 100 |
1 |
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|a Shevrin, L.N.
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| 245 |
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|a Semigroups and Their Subsemigroup Lattices
|h Elektronische Ressource
|c by L.N. Shevrin, A.J. Ovsyannikov
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| 250 |
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|a 1st ed. 1996
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 1996, 1996
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| 300 |
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|a XI, 380 p
|b online resource
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| 505 |
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|a A. Semigroups with Certain Types of Subsemigroup Lattices -- I. Preliminaries -- II. Semigroups with Modular or Semimodular Subsemigroup Lattices -- III. Semigroups with Complementable Subsemigroups -- IV. Finiteness Conditions -- V. Inverse Semigroups with Certain Types of Lattices of Inverse Subsemigroups -- VI. Inverse Semigroups with Certain Types of Lattices of Full Inverse Subsemigroups -- B. Properties of Subsemigroup Lattices -- VII. Lattice Characteristics of Classes of Semigroups -- VIII. Embedding Lattices in Subsemigroup Lattices -- C. Lattice Isomorphisms -- IX. Preliminaries on Lattice Isomorphisms -- X. Cancellative Semigroups -- XI. Commutative Semigroups -- XII. Semigroups Decomposable into Rectangular Bands -- XIII. Semigroups Defined by Certain Presentations -- XIV. Inverse Semigroups -- List of Notations -- List of Subsections Containing Unsolved Problems or Open Questions
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| 653 |
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|a Group Theory and Generalizations
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| 653 |
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|a Group theory
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| 653 |
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|a Mathematical logic
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| 653 |
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|a Algebra
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| 653 |
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|a Order, Lattices, Ordered Algebraic Structures
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| 653 |
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|a Mathematical Logic and Foundations
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| 700 |
1 |
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|a Ovsyannikov, A.J.
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Mathematics and Its Applications
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| 028 |
5 |
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|a 10.1007/978-94-015-8751-8
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| 856 |
4 |
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|u https://doi.org/10.1007/978-94-015-8751-8?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 512.2
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| 520 |
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|a 0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in the book [Suz] and the surveys [K Pek St], [Sad 2], [Ar Sad], there is also a quite recent book [Schm 2]. As another inspiring source, one should point out a branch of mathematics to which the book [Baer] was devoted. One of the key objects of examination in this branch is the subspace lattice of a vector space over a skew field. A more general approach deals with modules and their submodule lattices. Examining subsystem lattices for the case of modules as well as for rings and algebras (both associative and non-associative, in particular, Lie algebras) began more than thirty years ago; there are results on this subject also for lattices, Boolean algebras and some other types of algebraic systems, both concrete and general. A lot of works including several surveys have been published here
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