On prime and congruence-prime acts over monoid with zero (in Ukrainian)

Author Yu. T. Bilyak, H. V. Zelisko, M. Ya. Komarnitskiy
jbilyak@ukr.net, zelisko_halyna@yahoo.com, mykola_komarnytsky@yahoo.com
Ivan Franko Natonal University of Lviv

Abstract The properties of the prime and the congruence-prime acts over monoid with zero are investigated.
Keywords monoid; act; congruence; prime act; congruence-prime act; prime congruence
Reference 1. R.E. Johnson, Representations of prime rings, Trans. Amer. Math. Soc., 74 (1953), ¹2, 351-357.

2. V.À. Andrunakievich, Prime modules and Baer radical, Siberian Mathematical Journal, 2 (1961), ¹6, 801-806. (in Russian)

3. E.H. Feller, E.W. Swokowski, Prime modules, Can. J. Math., 17 (1965), 1041-1052.

4. H.I. Karakas, On Noetherian modules, Metu Journal of Pure and Applied Science, 5 (1972), 165-168.

5. J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.

6. V.À. Andrunakievich, Ju.M. Rjabuhin, Special modules and special radicals, Doklady Akademii Nauk, 147 (1962), ¹6, 1274-1277. (in Russian)

7. J. Beachy, Some aspects of noncommutative localization, Lect. Notes Math., 545 (1976), 2-31.

8. L. Bican, P. Jampor, T. Kepka, P. Nemec, Prime and coprime modules, Fund. Math., 57 (1980), 33-45.

9. D. Handelman, J. Lawrence, Strongly prime rings, Trans. Amer. Math. Soc., 211 (1975), 209-223.

10. R. Wisbauer, On prime modules and rings, Commun. Algebra, 11 (1983), 2249-2265.

11. E.N. Roiz, The Jacobson and Baer radicals of rings, and their multiplicative semigroups, Izv. Vyssh. Uchebn. Zaved. Mat., 10 (1975), 71-79. (in Russian)

12. J. Ahsan, L. Zhongkui, Prime and semiprime acts over monoids with zero, Math. J., Ibaraki Univ., 33 (2001), 9-15.

13. A.A. Estaji, S. Tajnia, Prime subacts over commutative monoids with zero, Lobachevskii Journal of Mathematics, 32 (2011), ¹4, 358-365.

14. H.J. Hoehuke, Uber das untere und obere Radikal einer Halbgruppe, Math. Z., 89 (1965), 300-311.

Pages 3-7
Volume 39
Issue 1
Year 2013
Journal Matematychni Studii
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