caa a22 4500 445344792 CHVBK 20180317142825.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00233-010-9255-9 doi (NATIONALLICENCE)springer-10.1007/s00233-010-9255-9 Congruence openings of additive Green's relations onasemiring [Elektronische Daten] [Nada Damljanović, Miroslav Ćirić, Stojan Bogdanović] In a series of papers, Green's relations on the additive and multiplicative reducts of a semiring proved to be a very useful tool in the study of semirings. However, in the vast majority of cases, Green's relations are not congruences, and we show that in such cases it is much more convenient to use the congruence openings of Green's relations, instead of the Green's relations themselves. By means of these congruence openings we define and study several very interesting operators on the lattices of varieties of semirings and additively idempotent semirings, and, in particular, we establish order embeddings of the lattice of varieties of additively idempotentsemirings into the direct products of the lattices of open (resp. closed) varieties with respect to two opening (resp. closure) operators on this lattice that we introduced. Springer Science+Business Media, LLC, 2010 Semiring nationallicence Semigroup nationallicence Green's relations nationallicence Congruence opening nationallicence Additively idempotent semiring nationallicence Varieties of semirings nationallicence Damljanović Nada Technical Faculty in Čačak, University of Kragujevac, Svetog Save 65, 32000, Čačak, Serbia aut Ćirić Miroslav Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia aut Bogdanović Stojan Faculty of Economics, University of Niš, Trg Kralja Aleksandra 11, 18000, Niš, Serbia aut Semigroup Forum Springer-Verlag 82/3(2011-06-01), 437-454 0037-1912 82:3<437 2011 82 233 https://doi.org/10.1007/s00233-010-9255-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-010-9255-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Damljanović Nada Technical Faculty in Čačak, University of Kragujevac, Svetog Save 65, 32000, Čačak, Serbia aut NATIONALLICENCE 700 1- Ćirić Miroslav Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia aut NATIONALLICENCE 700 1- Bogdanović Stojan Faculty of Economics, University of Niš, Trg Kralja Aleksandra 11, 18000, Niš, Serbia aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 82/3(2011-06-01), 437-454 0037-1912 82:3<437 2011 82 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer