scholarly journals The diameter of annihilator ideal graph of ℤn

2021 ◽  
Author(s):  
Ami Rahmawati ◽  
Vika Yugi Kurniawan ◽  
Supriyadi Wibowo
Keyword(s):  
Annihilator Ideal

Annihilator Ideal-Based Zero-Divisor Graphs Over Multiplication Modules

2013 ◽  
Vol 41 (3) ◽  
pp. 1134-1148 ◽  
Author(s):  
Ghalandarzadeh ◽  
S. Shirinkam ◽  
P. Malakooti Rad
Keyword(s):  
Zero Divisor ◽  
Annihilator Ideal

When the annihilator-ideal graph is planar or complete bipartite graph

2019 ◽  
Vol 12 (02) ◽  
pp. 1950024
Author(s):  
M. J. Nikmehr ◽  
S. M. Hosseini
Keyword(s):  
Commutative Ring ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Simple Graph ◽  
Annihilator Ideal ◽  
Vertex Set

Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be the set of ideals of [Formula: see text] with nonzero annihilator. The annihilator-ideal graph of [Formula: see text], denoted by [Formula: see text], is a simple graph with the vertex set [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we present some results on the bipartite, complete bipartite, outer planar and unicyclic of the annihilator-ideal graphs of a commutative ring. Among other results, bipartite annihilator-ideal graphs of rings are characterized. Also, we investigate planarity of the annihilator-ideal graph and classify rings whose annihilator-ideal graph is planar.

A Note on Quasi-Frobenius Rings and Ring Epimorphisms

1969 ◽  
Vol 12 (3) ◽  
pp. 287-292 ◽  
Author(s):  
H. H. Storrer
Keyword(s):  
Unit Element ◽  
Usual Condition ◽  
Annihilator Ideal ◽  
Frobenius Rings ◽  
Weakened Form

In this note, we characterize quasi-Frobenius rings by a weakened form of the usual condition, that every ideal is an annihilator ideal.We then apply this result to pure rings in the sense of Cohn and to dominant rings, a concept arising in the study of ring epimorphisms. All rings considered have a unit element.

Two notes on spectral synthesis for discrete Abelian groups

1965 ◽  
Vol 61 (3) ◽  
pp. 617-620 ◽  
Author(s):  
R. J. Elliott
Keyword(s):  
Fourier Transform ◽  
Dual Space ◽  
Fourier Transforms ◽  
Spectral Synthesis ◽  
Division Problem ◽  
Exponential Functions ◽  
Translation Invariant ◽  
Annihilator Ideal ◽  
The Fourier Transform ◽  
Translation Invariant Subspace

Introduction. Spectral synthesis is the study of whether functions in a certain set, usually a translation invariant subspace (a variety), can be synthesized from certain simple functions, exponential monomials, which are contained in the set. This problem is transformed by considering the annihilator ideal in the dual space, and after taking the Fourier transform the problem becomes one of deciding whether a function is in a certain ideal, that is, we have a ‘division problem’. Because of this we must take into consideration the possibility of the Fourier transforms of functions having zeros of order greater than or equal to 1. This is why, in the original situation, we study whether varieties are generated by their exponential monomials, rather than just their exponential functions. This viewpoint of the problem as a division question, of course, perhaps throws light on why Wiener's Tauberian theorem works, and is implicit in the construction of Schwartz's and Malliavin's counter examples to spectral synthesis in L1(G) (cf. Rudin ((4))).

scholarly journals More on the annihilator-ideal graph of a commutative ring

2019 ◽  
Vol 18 (08) ◽  
pp. 1950160
Author(s):  
M. J. Nikmehr ◽  
S. M. Hosseini
Keyword(s):  
Commutative Ring ◽  
Sufficient Conditions ◽  
Simple Graph ◽  
Necessary And Sufficient Conditions ◽  
Star Graph ◽  
Annihilator Ideal ◽  
Vertex Set ◽  
Necessary And Sufficient

Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be the set of ideals of [Formula: see text] with nonzero annihilator. The annihilator-ideal graph of [Formula: see text], denoted by [Formula: see text], is a simple graph with the vertex set [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we study the affinity between the annihilator-ideal graph and the annihilating-ideal graph [Formula: see text] (a well known graph with the same vertices and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text]) associated with [Formula: see text]. All rings whose [Formula: see text] and [Formula: see text] are characterized. Among other results, we obtain necessary and sufficient conditions under which [Formula: see text] is a star graph.

scholarly journals Leading terms of Artin L-series at negative integers and annihilation of higher K-groups

2011 ◽  
Vol 151 (1) ◽  
pp. 1-22 ◽  
Author(s):  
ANDREAS NICKEL
Keyword(s):  
Galois Group ◽  
Galois Extension ◽  
Number Fields ◽  
Ring Of Integers ◽  
Annihilator Ideal ◽  
Galois Action ◽  
Higher Dimensional ◽  
Totally Real ◽  
Tamagawa Number Conjecture ◽  
Special Case

AbstractLet L/K be a finite Galois extension of number fields with Galois group G. We use leading terms of Artin L-series at strictly negative integers to construct elements which we conjecture to lie in the annihilator ideal associated to the Galois action on the higher dimensional algebraic K-groups of the ring of integers in L. For abelian G our conjecture coincides with a conjecture of Snaith and thus generalizes also the well-known Coates–Sinnott conjecture. We show that our conjecture is implied by the appropriate special case of the equivariant Tamagawa number conjecture (ETNC) provided that the Quillen–Lichtenbaum conjecture holds. Moreover, we prove induction results for the ETNC in the case of Tate motives h0(Spec(L))(r), where r is a strictly negative integer. In particular, this implies the ETNC for the pair (h0(Spec(L))(r), ), where L is totally real, r < 0 is odd and is a maximal order containing ℤ[]G, and will also provide some evidence for our conjecture.

Baer Endomorphism Rings and Closure Operators

1978 ◽  
Vol 30 (5) ◽  
pp. 1070-1078 ◽  
Author(s):  
Soumaya M. Khuri
Keyword(s):  
Endomorphism Ring ◽  
Free Module ◽  
Linear Transformations ◽  
Endomorphism Rings ◽  
Dual Vector ◽  
Annihilator Ideal ◽  
Baer Ring ◽  
Left Annihilator ◽  
Torsion Free ◽  
Made In

A Baer ring is a ring in which every right (and left) annihilator ideal is generated by an idempotent. Generalizing quite naturally from the fact that the endomorphism ring of a vector space is a Baer ring, Wolfson [5; 6] investigated questions such as when the endomorphism ring of a free module is a Baer ring, and when the ring of continuous linear transformations on a pair of dual vector spaces is a Baer ring. A further generalization was made in [7], where the question of when the endomorphism ring of a torsion-free module over a semiprime left Goldie ring is a Baer ring was treated.

ON ANNIHILATOR IDEALS OF C-ALGEBRAS

2013 ◽  
Vol 06 (01) ◽  
pp. 1350009
Author(s):  
M. SAMBASIVA RAO
Keyword(s):  
Boolean Algebra ◽  
Complete Boolean Algebra ◽  
C Algebra ◽  
C Algebras ◽  
Annihilator Ideal ◽  
Equivalent Conditions

The concept of annihilator ideals is introduced in C-algebras. Some properties of these annihilator ideals are studied and then proved that the class of all annihilator ideals forms a complete Boolean algebra. A set of equivalent conditions are obtained for every ideal of a C-algebra to become an annihilator ideal. Some properties of homomorphic images and inverse images of annihilators ideals of a C-algebra are studied.

On the BP-homology of 2e × 2e

2008 ◽  
Vol 3 (3) ◽  
pp. 409-435
Author(s):  
Leticia Zárate
Keyword(s):  
Formal Group ◽  
Minimal System ◽  
Easy Consequence ◽  
Annihilator Ideal ◽  
Formal Group Law ◽  
Minimal System Of Generators ◽  
Divisibility Properties ◽  
Group Law

AbstractWe study υ0- and υ1-divisibility properties of the [2e]-series associated to the universal 2-typical formal group law. This allows us to identify elements annihilating the toral class τ in BP*(2e × 2e). We conjecture that these elements form a minimal system of generators of the annihilator ideal of τ. This would provide a Landweber-type presentation for the BP-homology of 2e × 2e from which the relation hom:dimBP (Z2e × Z2e) = 2 would be an easy consequence.

Sign in / Sign up

Export Citation Format

Share Document