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Graded weakly 1-absorbing primary ideals

Demonstratio Mathematica, 2023
Let GG be a group and RR be a GG-graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is a generalization of graded 1-absorbing primary ideal.
Bataineh Malik, Abu-Dawwas Rashid
doaj   +3 more sources

Some notes on graded weakly 1-absorbing primary ideals

Demonstratio Mathematica, 2023
A proper graded ideal PP of a commutative graded ring RR is called graded weakly 1-absorbing primary if whenever x,y,zx,y,z are nonunit homogeneous elements of RR with 0≠xyz∈P0\ne xyz\in P, then either xy∈Pxy\in P or zz is in the graded radical of PP. In
Alshehry Azzh Saad, Abu-Dawwas Rashid, Al-Rashdan Majd   +2 more
doaj   +2 more sources

Graded Weakly Strongly Quasi-Primary Ideals over Commutative Graded Rings

Mathematics
In this article, we introduce and examine the concept of graded weakly strongly quasi primary ideals. A proper graded ideal P of R is said to be a graded weakly strongly quasi primary (shortly, Gwsq-primary) ideal if whenever 0≠xy∈P, for some homogeneous
Azzh Saad Alshehry, Rashid Abu-Dawwas, Basel Hawary   +2 more
doaj   +2 more sources

On Graded 2-Prime Ideals

Mathematics, 2021
The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different.
Malik Bataineh, Rashid Abu-Dawwas
doaj   +1 more source

On graded WAG2-absorbing submodule

Математичні Студії, 2022
Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded $WAG2$-absorbing submodule. A number of results concerning of these classes of graded submodules
K. Al-Zoubi, Mariam Al-Azaizeh
doaj   +1 more source

Castelnuovo-Mumford regularity and extended degree [PDF]

, 2002
The main result of this paper shows that the Castelnuovo-Mumford regularity of the tangent cone of a local ring is effectively bounded by the dimension and any extended degree.
Rossi, Maria Evelina, Trung, Ngo Viet, Valla, Giuseppe   +2 more
core   +3 more sources

Hodge ideals and spectrum of isolated hypersurface singularities [PDF]

, 2020
We introduce Hodge ideal spectrum for isolated hypersurface singularities to see the difference between the Hodge ideals and the microlocal $V$-filtration modulo the Jacobian ideal.
Jung, Seung-Jo, Kim, In-Kyun, Saito, Morihiko, Yoon, Youngho   +3 more
core   +3 more sources

ON GRADED 2-ABSORBING PRIMARY AND GRADED WEAKLY 2-ABSORBING PRIMARY IDEALS

Journal of the Korean Mathematical Society, 2017
Summary: Let \(G\) be a group with identity \(e\) and let \(R\) be a \(G\)-graded ring. In this paper, we introduce and study graded 2-absorbing primary and graded weakly 2-absorbing primary ideals of a graded ring which are different from 2-absorbing primary and weakly 2-absorbing primary ideals.
Al-Zoubi, Khaldoun, Sharafat, Nisreen
openaire   +3 more sources

Character groups of Hopf algebras as infinite-dimensional Lie groups [PDF]

, 2015
In this article character groups of Hopf algebras are studied from the perspective of infinite-dimensional Lie theory. For a graded and connected Hopf algebra we construct an infinite-dimensional Lie group structure on the character group with values in ...
Bogfjellmo, Geir, Dahmen, Rafael, Schmeding, Alexander   +2 more
core   +3 more sources

Products of ideals may not be Golod [PDF]

, 2016
We exhibit an example of a product of two proper monomial ideals such that the residue class ring is not Golod. We also discuss the strongly Golod property for rational powers of monomial ideals, and introduce some sufficient conditions for weak ...
De Stefani, Alessandro
core   +2 more sources