## Basic pseudorings.(English)Zbl 1203.06012

The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using the term operation called Sasaki projection. We give a mutual relationship between basic algebras and basic pseudorings. We characterize the basic pseudorings that can be converted into orthomodular lattices.

### MSC:

 06D35 MV-algebras 03G25 Other algebras related to logic 06C15 Complemented lattices, orthocomplemented lattices and posets

### Keywords:

basic algebra; basic pseudoring; orthomodular lattice
Full Text:

### References:

 [1] Beran, L.: Orthomodular Lattices. Reidel Publ., Dordrecht, 1985. · Zbl 0583.06008 [2] Birkhoff, G.: Lattice Theory. Publ. AMS, Providence, 1967. · Zbl 0153.02501 [3] Chajda, I., Halaš, R., Kühr, J.: Semilattice Structures. Heldermann Verlag, Lemgo, 2007. · Zbl 1117.06001 [4] Chajda, I., Kolařík, M.: Independence of axiom system of basic algebras. Soft Computing 13, 1 (2009), 41-43. · Zbl 1178.06007 [5] Chajda, I., Länger, H.: Ring-like structures corresponding to MV-algebras via symmetrical difference. Sitzungsberichte ÖAW, Math.-Naturw. Kl. Abt. II 213 (2004), 33-41. · Zbl 1116.06012 [6] Dorfer, G., Dvurečenskij, A., Länger H.: Symmetric difference in orthomodular lattices. Math. Slovaca 46 (1996), 435-444. · Zbl 0890.06006 [7] Dorninger, D., Länger, H., Maczyński, M.: The logic induced by a system of homomorphisms and its various algebraic characterizations. Demonstratio Math. 30 (1997), 215-232. · Zbl 0879.06005 [8] Dorninger, D., Länger, H., Maczyński, M.: On ring-like structures occuring in axiomatic quantum mechanics. Sitzungsberichte ÖAW, Math.-Naturw. Kl. Abt. II 206 (1997), 279-289. · Zbl 0945.03095 [9] Dorninger, D., Länger, H., Maczyński, M.: Lattice properties of ring-like quantum logics. Intern. J. of Theor. Physics 39 (2000), 1015-1026. · Zbl 0967.03055 [10] Shang, Y.: Ring-like structures corresponding to pseudo MV-algebras. Soft Computing 13, 1 (2009), 71-76. · Zbl 1165.06005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.