148 citations
- Research Institute for Astronomy and Astrophysics of MaraghIR63 papers
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9 papers · 1 filter
On the ideal avoidance property
Justin Chen, Abolfazl Tarizadeh
In this article, we investigate the avoidance property of ideals and rings. Among the main results, a general version of the avoidance lemma is formulated. It is shown that every i…
Avoidance and Absorbance
Abolfazl Tarizadeh, Justin Chen
We study the two dual notions of prime avoidance and prime absorbance. We generalize the classical prime avoidance lemma to radical ideals. A number of new criteria are provided fo…
On the polymatroidal property of monomial ideals with a view towards orderings of minimal generators
Somayeh Bandari, Rahim Rahmati-Asghar
We prove that a monomial ideal generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal…
Structural results on lifting, orthogonality and finiteness of idempotents
Abolfazl Tarizadeh, Pramod K. Sharma
In this paper, using the canonical correspondence between the idempotents and clopens, we obtain several new results on lifting idempotents. The Zariski clopens of the maximal spec…
Notes on finitely generated flat modules
Abolfazl Tarizadeh
In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtain…
A fresh look into monoid rings and formal power series rings
Abolfazl Tarizadeh
In this article, the ring of polynomials is studied in a systematic way through the theory of monoid rings. As a consequence, this study provides natural and canonical approaches i…