The strongly irreducible dimension of rings vs. the derived dimension of the space of strongly irreducible ideals with V-topology

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

Abstract

An ideal $I$ of a ring $R$ is called strongly irreducible ideal (SI-ideal, for short), whenever the inclusion $J\cap K\subseteq I$, implies that $J\subseteq I$ or $K\subseteq I$. Let $X={\rm SSpec}(R)$ be the set of all strongly irreducible ideals of a ring $R$. Then $X$ with certain topology has derived dimension if and only if $R$ has strongly irreducible dimension. Moreover, the two dimensions differ by at most $1$.

Keywords

References

[1] A. Azizi, Strongly irreducible ideals, J. Aust. Math. Soc., 84 No. 2 (2008) 145-154.
[2] K. R. Goodearl and R. B. Warfield, An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, 2004.
[3] J. Hashemi and F. Hassanzadeh, Some remarks on strongly irreducible ideals, J. Math. Ext., To appear.
[4] O. A. S. Karamzadeh, On the classical Krull dimension of rings, Fund. Math., 117 No. 2 (1983) 103-108.
[5] G. Krause, On fully left bounded left noetherian rings, J. Algebra., 23 No. 1 (1972) 88-99.
[6] M. Namdari, The story of rings of continuous functions in Ahvaz: From C(X) to Cc(X), J. Iran. Math. Soc., 4 No. 2 (2023) 149-177.
Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 03 October 2024

Files

Share

How to cite

Statistics