Almost zip Bezout domain

  • O.M. Romaniv Ivan Franko National University of Lviv
  • B.V. Zabavsky Ivan Franko National University of Lviv
Keywords: Bezout ring, elementary divisor ring, almost zip ring, Kasch ring, J-Noetherian ring, Goldie ring, maximal ideal, prime ideal

Abstract

J. Zelmanowitz introduced the concept of a ring, which we call a zip ring. In this paper we characterize a commutative Bezout domain whose finite homomorphic images are zip rings modulo its nilradical.

Author Biographies

O.M. Romaniv, Ivan Franko National University of Lviv

Associate Professor,
Department of Algebra and Logic,
Faculty of Mechanics and Mathematics,
Ivan Franko National University of Lviv

B.V. Zabavsky, Ivan Franko National University of Lviv

Department of Algebra and Logic, Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv

References

Anderson D. A note on minimal prime ideals, Proc. Amer. Math. Soc. 1994, 122 (1), 13–14.

Estes D., Ohm J. Stable range in commutative rings, J. Alg. 1967, 7 (3), 343–362.

De Marco G. Projectivity of pure ideals, Rendic. Sem. Matem. Univ. Pad. 1983, 69, 289–304.

Faith C. Rings with zero intersection property on annihilators: zip rings, Publ. Matem. 1989, 33 (2), 329–338.

Kaplansky I. Elementary divisors and modules, Trans. Amer. Math. Soc. 1949, 66, 464–491.

Kaplansky I. Commutative rings, Univ. of Chicago Press, Chicago, IL, 1974.

Matlis E. Commutative semi-coherent and semi-regular rings, J. Alg. 1985, 95, 343–372.

Shores T., Wiegand R. Decompositions of modules and matrices, Bull. Amer. Math. Soc. 1973, 79 (6), 1277–1280.

Zabavsky B. Fractionally regular Bezout rings, Matem. Stud. 2009, 32 (1), 76–80.

Zelmanowitz J. The finite intersection property on annihilator right ideals, Proc. Amer. Math. Soc. 1976, 57 (2), 213–216.

Published
2020-06-19
How to Cite
1.
Romaniv O, Zabavsky B. Almost zip Bezout domain. Mat. Stud. [Internet]. 2020Jun.19 [cited 2020Sep.26];53(2):115-8. Available from: http://matstud.org.ua/ojs/index.php/matstud/article/view/82
Section
Articles