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On The Coset Structure Of Skew Lattices
Published on Nov 12, 20123740 Views
The study of noncommutative lattices began in 1949 with Pascual Jordan, motivated by questions on Quantum Logic. Skew lattices have been the most successful variation of noncommutative lattices. Jonat
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On The Coset Structure Of Skew Lattices00:00
Motivations00:20
Authors00:50
Algebraic Structure of Skew Lattices02:26
Relations - 102:28
Relations - 202:35
Equivalences - 102:46
Relations - 303:17
Equivalences - 203:20
Equivalences - 303:38
Preorders03:56
Partially ordered sets04:19
Totally ordered sets04:57
Partial Orders05:16
Order Structure of Lattices - 106:10
Algebraic Structure of Lattices - 107:20
Algebraic Structure of Lattices - 209:18
Algebraic Structure of Skew Lattices09:54
S enriched with S11 to S14 is equivalent to L10:21
Examples of Skew Lattices - 110:54
Examples of Skew Lattices - 211:00
Implications11:29
Skew Lattices in Rings of Matrices12:58
Skew Lattices of Partial Functions - 113:44
Skew Lattices of Partial Functions - 214:44
Skew Lattices of Partial Functions - 314:50
Skew Lattices of Partial Functions - 414:56
Skew Lattices of Partial Functions - 515:09
Skew Lattices of Partial Functions - 615:29
Skew Lattices of Partial Functions - 715:49
Skew Lattices of Partial Functions - 815:54
Rectangular & Order Structure of Skew Lattices16:50
Rectangular Structure of Skew Lattices - 117:09
Rectangular Structure of Skew Lattices - 217:43
Order, Congruence and Hasse Diagram - 118:26
Order, Congruence and Hasse Diagram - 220:04
Order, Congruence and Hasse Diagram - 320:35
Order, Congruence and Hasse Diagram - 421:12
Order, Congruence and Hasse Diagram - 521:48
Leech’s 1st decomposition Theorem - 123:40
Leech’s 1st decomposition Theorem - 225:30
Leech’s 1st decomposition Theorem - 326:38
Varieties of Skew Lattices - 127:36
Varieties of Lattices27:58
Varieties of Skew Lattices - 228:54
Varieties of Skew Lattices - 329:30
Varieties of Skew Lattices - 429:44
Varieties of Skew Lattices - 530:54
Skew Boolean Algebras - 131:46
Skew Boolean Algebras - 233:24
Coset Structure Decomposition34:21
Coset Structure Theorem (Leech 1993)35:56
Coset Structure - 137:31
Coset Structure - 237:34
Coset Structure Theorem (Leech 1993) - 137:45
Coset Structure - 338:45
Coset Structure - 439:00
Coset Structure Theorem (Leech 1993) - 239:06
Transversal of Cosets - 139:13
Transversal of Cosets - 239:15
Transversal of Cosets - 339:33
Transversal of Cosets - 439:40
Coset Structure Theorem (Leech 1993) - 340:02
Coset Structure Theorem (Leech 1993) - 440:20
Coset Structure Theorem (Leech 1993) - 540:24
Coset Laws Characterization40:36
Coset Laws for Cancellative Skew Lattices - 140:37
Coset Laws for Cancellative Skew Lattices - 241:08
Coset Laws for Skew Lattices in Rings42:37
Combinatorial Consequences42:59
Index and Order of a Coset - 142:59
Index and Order of a Coset - 243:40
Index Theorems for Finite Skew Lattices - 144:04
Index Theorems for Finite Skew Lattices - 244:20
Overview - 145:16
Overview - 245:17
Dualities for Skew Lattices47:18
Hvala / Thank you / Obrigado48:06