Zariski Topologies on Graded Ideals-Reference-Cited by-同舟云学术

Zariski Topologies on Graded Ideals

Published:2021-10-01 Issue:1 Volume:78 Page:215-224
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Bataineh Malik¹,Alshehry Azzh Saad²,Abu-Dawwas Rashid³

Affiliation:

1. 1 Department of Mathematics and Statistics, Jordan University of Science and Technology , Irbid , JORDAN

2. 2 Department of Mathematics, Princess Nourah University Riyadh , Riyadh SAUDI ARABIA

3. 3 Department of Mathematics, Yarmouk University , Irbid , JORDAN

Abstract

Abstract In this paper, we show there are strong relations between the algebraic properties of a graded commutative ring R and topological properties of open subsets of Zariski topology on the graded prime spectrum of R. We examine some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense, and irreducible. We also present a characterization for the radical of a graded ideal in R by using topological properties.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2021-0015

Reference9 articles.

1. [1] ABU-DAWWAS, R.: Zariski topology on the spectrum of graded pseudo prime submodules, Bol. Soc. Parana. Mat. 39 (2021), no. 3, 17–26.

2. [2] ABU-DAWWAS, R.—BATAINEH, M.: Graded r-ideals, Iranian J. Math. Sci. Inform. 14 (2019), no. 2, 1–8.

3. [3] AL-ZOUBI, K.—JARADAT M.: The Zariski topology on the graded classical prime spectrum of a graded module over a graded commutative ring, Mat. Vesnik, 70 (2018), no. 4, 303–313.

4. [4] AL-ZOUBI, K.—JARADAT M.: The Zariski topology on the graded primary spectrum over graded commutative ring, Tatra Mt. Math. Publ. 74 (2019), 7–16.

5. [5] FARZALIPOUR, F.—GHIASVAND, P.: On the union of graded prime submodules, Thai J. Math. 9 (2011), no. 1, 49–55.