Results 1 to 10 of about 1,293 (84)
ON $(m,n)$-CLOSED IDEALS IN AMALGAMATED ALGEBRA
International Electronic Journal of Algebra, 2021 Let R be a commutative ring with 1 6= 0 and let m and n be integers with 1 ≤ n < m. A proper ideal I of R is called an (m,n)-closed ideal of R if whenever am ∈ I for some a ∈ R implies an ∈ I. Let f : A → B be a ring homomorphism and let J be an ideal of
Mohammed Issoual +2 more
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SOME PROPERTIES OF STAR OPERATIONS ON RING EXTENSIONS
International Electronic Journal of Algebra, 2021 Let ? be a star operation on a ring extension R ⊆ S. A ring extension R ⊆ S is called Prüfer star-multiplication extension (P?ME) if (R[m],m[m]) is a Manis pair in S for every ?-maximal ideal m of R [L. Paudel and S.
Lokendra Paudel, S. Tchamna
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On the Genus of the Idempotent Graph of a Finite Commutative Ring
Discussiones Mathematicae - General Algebra and Applications, 2021 Let R be a finite commutative ring with identity. The idempotent graph of R is the simple undirected graph I(R) with vertex set, the set of all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = 0.
Belsi G. Gold, Kavitha S., Selvakumar K.
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ON THE DOT PRODUCT GRAPH OF A COMMUTATIVE RING II [PDF]
, 2020 In 2015, the second-named author introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 ≤ n < ∞ be an integer, and R = A × A × · · · × A (n times).
M. Abdulla, Ayman Badawi
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On nonnil-coherent modules and nonnil-Noetherian modules
Open Mathematics, 2022 In this article, we introduce two new classes of modules over a ϕ\phi -ring that generalize the classes of coherent modules and Noetherian modules. We next study the possible transfer of the properties of being nonnil-Noetherian rings, ϕ\phi -coherent ...
Haddaoui Younes El +2 more
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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
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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 +2 more
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On 2r-ideals in commutative rings with zero-divisors
Open Mathematics, 2023 In this article, we are interested in uniformly prpr-ideals with order ≤2\le 2 (which we call 2r2r-ideals) introduced by Rabia Üregen in [On uniformly pr-ideals in commutative rings, Turkish J. Math. 43 (2019), no. 4, 18781886]. Several characterizations
Alhazmy Khaled +3 more
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Noetherian properties in composite generalized power series rings
Open Mathematics, 2020 Let (Γ,≤)({\mathrm{\Gamma}},\le ) be a strictly ordered monoid, and let Γ⁎=Γ\{0}{{\mathrm{\Gamma}}}^{\ast }\left={\mathrm{\Gamma}}\backslash \{0\}. Let D⊆ED\subseteq E be an extension of commutative rings with identity, and let I be a nonzero proper ...
Lim Jung Wook, Oh Dong Yeol
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Extended Annihilating-Ideal Graph of a Commutative Ring
Discussiones Mathematicae - General Algebra and Applications, 2022 Let R be a commutative ring with identity. An ideal I of a ring R is called an annihilating-ideal if there exists a nonzero ideal J of R such that IJ = (0) and we use the notation 𝔸(R) for the set of all annihilating-ideals of R.
Nithya S., Elavarasi G.
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