Page 8 - Leech, Jonathan E. 2020. Noncommutative Lattices: Skew Lattices, Skew Boolean Algebras and Beyond. Koper: University of Primorska Press
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FURTHER TOPICS IN SKEW LATTICES ................................................................. 163
5.1 Symmetric skew lattices ..................................................................................................... 166
5.2 Distributive identities in the symmetric case ............................................................. 169
5.3 Cancellation in skew lattices ............................................................................................. 171
5.4 Categorical skew lattices .................................................................................................... 178
5.5 Distributive skew lattices ................................................................................................... 187
5.6 Midpoints and distributive skew chains ....................................................................... 195
5.7 Counting theorems and cancellative skew lattices .................................................... 200
References ...................................................................................................................................... 206
VI: SKEW LATTICES IN RINGS ........................................................................................ 207
6.1 Quadratic skew lattices in rings ....................................................................................... 209
6.2 ∇ -bands and cubic skew lattices ...................................................................................... 219
6.3 The question of s -closure ................................................................................................. 230
6.4 Idempotent-closed rings ..................................................................................................... 233
6.5 Decomposing E(R) and R ..................................................................................................... 243
6.6 Idempotent-closed rings of matrices .............................................................................. 251
References ...................................................................................................................................... 259
VII: FURTHER TOPICS IN SKEW BOOLEAN ALGEBRAS .......................................... 261
7.1 Differences, discriminators and connections with other algebras ...................... 262
References ...................................................................................................................................... 272
Bibliography ......................................................................................................................... 275
Addendum 2020 ................................................................................................................. 281
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5.1 Symmetric skew lattices ..................................................................................................... 166
5.2 Distributive identities in the symmetric case ............................................................. 169
5.3 Cancellation in skew lattices ............................................................................................. 171
5.4 Categorical skew lattices .................................................................................................... 178
5.5 Distributive skew lattices ................................................................................................... 187
5.6 Midpoints and distributive skew chains ....................................................................... 195
5.7 Counting theorems and cancellative skew lattices .................................................... 200
References ...................................................................................................................................... 206
VI: SKEW LATTICES IN RINGS ........................................................................................ 207
6.1 Quadratic skew lattices in rings ....................................................................................... 209
6.2 ∇ -bands and cubic skew lattices ...................................................................................... 219
6.3 The question of s -closure ................................................................................................. 230
6.4 Idempotent-closed rings ..................................................................................................... 233
6.5 Decomposing E(R) and R ..................................................................................................... 243
6.6 Idempotent-closed rings of matrices .............................................................................. 251
References ...................................................................................................................................... 259
VII: FURTHER TOPICS IN SKEW BOOLEAN ALGEBRAS .......................................... 261
7.1 Differences, discriminators and connections with other algebras ...................... 262
References ...................................................................................................................................... 272
Bibliography ......................................................................................................................... 275
Addendum 2020 ................................................................................................................. 281
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