EMIS ELibM Electronic Journals Publications de l’Institut Mathématique, Nouvelle Série
Vol. 100[114], No. 1/1, pp. 87–93 (2016)

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DISTRIBUTIVE LATTICES OF JACOBSON RINGS

Yong Shao, Siniša Crvenković, Melanija Mitrović

School of Mathematics, Northwest University, Xian, P.R. China; Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia; Faculty of Mechanical Engineering, University of Niš, Niš, Serbia

Abstract: We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.

Keywords: semiring; distributive lattice; Jacobson ring; Mal’cev product; congruence

Classification (MSC2000): 16Y60; 08B05; 20M07

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Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.

© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition