caa a22 4500 445813695 CHVBK 20180317145219.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s11083-010-9152-6 doi (NATIONALLICENCE)springer-10.1007/s11083-010-9152-6 Cīrulis Jānis Department of Computing, University of Latvia, Raiņa b. 19, 1586, Riga, Latvia aut Nearlattices with an Overriding Operation [Elektronische Daten] [Jānis Cīrulis] A nearlattice A is a meet semilattice in which every initial segment is a lattice; A is said to be Boolean if all of these lattices are Boolean. Overriding on A is a binary operation $\triangleleft$ defined by $ a \triangleleft {b} := \sup\{x\colon (x \le a \mbox{ and } x {\mathrel{\mbox{\,\raisebox{.7ex}{$\scriptstyle|$}\hspace{-.75ex}\raisebox{-.35ex}{$\circ$}}}}b) \mbox{ or } x \le b\} $, where $x{\mathrel{\mbox{\,\raisebox{.7ex}{$\scriptstyle|$}\hspace{-.75ex}\raisebox{-.35ex}{$\circ$}}}}b$ means that the join of x and b exists. In particular, ${\triangleleft}$ extends the partial join operation. Natural examples of overriding nearlattices are provided by trees and by appropriate algebras of partial functions. In the paper, elementary properties of overriding are studied, an axiomatic description of it is obtained, and several results concerning associativity of the operation and the structure of function nearlattices with overriding are presented. The main result is a representation theorem (in terms of algebras of partial functions) for Boolean nearlattices with associative overriding. Springer Science+Business Media B.V., 2010 Flat poset nationallicence Nearlattice nationallicence Overriding nationallicence Semilattice nationallicence Subdirectly irreducible nationallicence Subdirect product nationallicence Tree nationallicence Order Springer Netherlands 28/1(2011-03-01), 33-51 0167-8094 28:1<33 2011 28 11083 https://doi.org/10.1007/s11083-010-9152-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9152-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cīrulis Jānis Department of Computing, University of Latvia, Raiņa b. 19, 1586, Riga, Latvia aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/1(2011-03-01), 33-51 0167-8094 28:1<33 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer