On the centroid of prime semirings

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

We define and study the extended centroid of a prime semiring. We show that the extended centroid is a semifield and give some properties of the centroid of a right multiplicatively cancellable prime semiring.

Anahtar Kelimeler:

Semiring, prime ideal, prime semiring, quotient semiring

On the centroid of prime semirings

Keywords:

Semiring, prime ideal, prime semiring, quotient semiring,

PDF

___

Beidar, K. I., Martindale III, W. S. and Mikhalev, A.V.: Rings with Generalized Identities, Marcel Dekker, Inc. (1996)
Golan, J. S.: Semirings and Their Applications, Kluwer Academic Publishers (1999).
Dedekind, R.: ¨ Uber die Theorie der ganzen algebraischen Zahlen, Supplement XI to P. G. Lejeune Dirichlet: Vorlesungen ¨ uber Zahlentheorie, 4 Auﬂ., Druck und Verlag, Braunschweig, 1894.
Hilbert, D: ¨ Uber den Zahlbegriﬀ, Jber. Detsch. Math.-Verein 8, 180-184 (1899).
Hungtington, E. V.: Complete sets of postulates for the theories of positive integral and positive rational numbers, Trans. Amer. Math. Soc. 3, 280-284 (1902).
Krull, W.: Axiomatische Begr¨ undung der Algemeinen Idealtheory, SitZ. phys.-med. Soc. Erlangen 56, 47-63 (1924). Lorenzen, P.: Abstrakte Begr¨ undung der multiplikativen Idealtheory, Math. Z. 45, 533-553 (1939).
Macaulay, F. S.: Algebraic Theory of Modular Systems, Cambridge University Press, Cambridge 1916.
Martindale, W. S.: Prime rings satisfying a generalized polynomial identity, J. Algebra 12, 576-584 (1969).
Noether, E.: Abstrakter Aufbau der Idealtheory in algebraischen Zahl und Funktionenk¨orpern, Math. Ann. 96, 26-61 (1927).
¨ Ozt¨ urk, M. A. and Jun, Y. B.: On the centroid of the prime gamma rings, Comm. Korean Math. Soc. 15(3), 469-479 (2000).
¨ Ozt¨ urk, M. A. and Jun, Y. B.: On the centroid of the prime gamma rings II, Turk. J. Math. 25(3), 367-377 (2001).