Geodesic
Orthorings
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 137-147.

Voir la notice de l'article provenant de la source Library of Science

Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.
Keywords: ortholattice, generalized ortholattice, sectionally complemented lattice, orthoring, arithmetical variety, weakly regular variety, congruence kernel, ideal term, basis of ideal terms, subtractive term 
@article{DMGAA_2004_24_1_a9,
     author = {Chajda, Ivan and L\"anger, Helmut},
     title = {Orthorings},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {137--147},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a9/}
}
TY  - JOUR
AU  - Chajda, Ivan
AU  - Länger, Helmut
TI  - Orthorings
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2004
SP  - 137
EP  - 147
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a9/
LA  - en
ID  - DMGAA_2004_24_1_a9
ER  - 
%0 Journal Article
%A Chajda, Ivan
%A Länger, Helmut
%T Orthorings
%J Discussiones Mathematicae. General Algebra and Applications
%D 2004
%P 137-147
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a9/
%G en
%F DMGAA_2004_24_1_a9
Chajda, Ivan; Länger, Helmut. Orthorings. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 137-147. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a9/

[1] G. Birkhoff, Lattice Theory, third edition, AMS Colloquium Publ. 25, Providence, RI, 1979.

[2] I. Chajda, Pseudosemirings induced by ortholattices, Czechoslovak Math. J. 46 (1996), 405-411.

[3] I. Chajda and G. Eigenthaler, A note on orthopseudorings and Boolean quasirings, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 83-94.

[4] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo 2003.

[5] I. Chajda and H. Länger, Ring-like operations in pseudocomplemented semilattices, Discuss. Math. Gen. Algebra Appl. 20 (2000), 87-95.

[6] I. Chajda and H. Länger, Ring-like structures corresponding to MV-algebras via symmetric difference, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, to appear.

[7] I. Chajda, H. Länger and M. Maczyński, Ring-like structures corresponding to generalized orthomodular lattices, Math. Slovaca 54 (2004), 143-150.

[8] G. Dorfer, A. Dvurecenskij and H. Länger, Symmetric difference in orthomodular lattices, Math. Slovaca 46 (1996), 435-444.

[9] D. Dorninger, H. Länger and M. Maczyński, The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232.

[10] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures occurring in axiomatic quantum mechanics, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279-289.

[11] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures induced by Mackey's probability function, Rep. Math. Phys. 43 (1999), 499-515.

[12] D. Dorninger, H. Länger and M. Maczyński, Lattice properties of ring-like quantum logics, Intern. J. Theor. Phys. 39 (2000), 1015-1026.

[13] D. Dorninger, H. Länger and M. Maczyński, Concepts of measures on ring-like quantum logics, Rep. Math. Phys. 47 (2001), 167-176.

[14] D. Dorninger, H. Länger and M. Maczyński, Ring-like structures with unique symmetric difference related to quantum logic, Discuss. Math. General Algebra Appl. 21 (2001), 239-253.

[15] G. Grätzer, General Lattice Theory, second edition, Birkhäuser Verlag, Basel 1998.

[16] J. Hedlíková, Relatively orthomodular lattices, Discrete Math. 234 (2001), 17-38.

[17] M. F. Janowitz, A note on generalized orthomodular lattices, J. Natur. Sci. Math. 8 (1968), 89-94.

[18] H. Länger, Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 97-105.

[19] H. Werner, A Mal'cev condition for admissible relations, Algebra Universalis 3 (1973), 263.