On ternary semifields

• Autorzy: Tapan K. Dutta , Sukhendu Kar
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce the notion of ternary semi-integral domain and ternary semifield and study some of their properties.In particular we also investigate the maximal ideals of the ternary semiring Z¯₀.

Słowa kluczowe

EN

ternary semiring; prime ideal; maximal ideal; ternary semi-integral domain; ternary division semiring; ternary semifield

Kategorie tematyczne

• 16Y60: Semirings
• 16Y30: Near-rings
• 20N10: Ternary systems (heaps, semiheaps, heapoids, etc.)

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2004
• Tom: 24
• Numer: 2
• Strony: 185-198

Daty

wydano

2004

otrzymano

2004-01-13

poprawiono

2004-07-19

poprawiono

2004-11-29

Twórcy

autor

Tapan K. Dutta

• Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India

autor

Sukhendu Kar

• Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India

Bibliografia

• [1] T.K. Dutta and S. Kar, On regular ternary semirings, Advances in Algebras, World Scientific Publ., Singapore 2003, 343-355.
• [2] T.K. Dutta and S. Kar, On the Jacobson radical of a ternary semiring, Southeast Asian Bull. Math. 28 (2004), 1-13.
• [3] T.K. Dutta and S. Kar, On prime ideals and prime radical of ternary semirings, Bull. Calcutta Math. Soc. 97 (2005), to appear.
• [4] T.K. Dutta and S. Kar, On semiprime ideals and irreducible ideals of ternary semirings, (in preparation).
• [5] J.S. Golan, Semirings and their Applications, Kluwer Academic Publishers, Dordrecht 1999.
• [6] U. Hebisch and H.J. Weinert, Semirings - Algebraic Theory and Applications in Computer Science, World Scientific Publ. Co. Inc., River Edge, NJ, 1998.
• [7] D.H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math. 59 (1932), 329-338.
• [8] W.G. Lister, Ternary rings, Trans. Amer. J. Math. Soc. 154 (1971), 37-55.
• [9] J. Łoś, On the extending of models I, Fund. Math. 42 (1955), 38-54.
• [10] M.L. Santiago, Some contributions to the study of ternary semigroups and semiheaps, Ph.D. Thesis, University of Madras 1983.
• [11] M.K. Sen and M.R. Adhikari, On maximal k-ideals of semirings, Proc. Amer. Math. Soc. 118 (1993), 699-703.

Identyfikatory

DOI

10.7151/dmgaa.1084