scholarly journals Annihilator graph of semiring of matrices over Boolean semiring

2020 ◽  
Vol 1494 ◽  
pp. 012009
Author(s):  
R Yudatama ◽  
V Y Kurniawan ◽  
S B Wiyono
Keyword(s):  
Boolean Semiring ◽  
Annihilator Graph

scholarly journals Zero annihilator graph of semiring of matrices over Boolean semiring

2021 ◽  
Author(s):  
Haniiam Mariiaa ◽  
Vika Yugi Kurniawan ◽  
Sutrima
Keyword(s):  
Boolean Semiring ◽  
Annihilator Graph

Some Properties of Annihilator Graph of a Commutative Ring

2014 ◽  
Vol 10 (5) ◽  
pp. 61-68
Author(s):  
Priyanka Pratim Baruah ◽  
◽  
Kuntala Patra
Keyword(s):  
Commutative Ring ◽  
Annihilator Graph

Maximal k-ideals and r-ideals in semirings

2015 ◽  
Vol 14 (10) ◽  
pp. 1250195 ◽  
Author(s):  
Song-Chol Han
Keyword(s):  
Congruence Class ◽  
Special Kind ◽  
Equivalent Condition ◽  
Idempotent Semiring ◽  
Boolean Semiring

Some properties of (left) k-ideals and r-ideals of a semiring are considered by the help of the congruence class semiring. It is proved that a proper k-ideal of a semiring with an identity is prime if it is a maximal left k-ideal. An equivalent condition for a proper r-ideal of a semiring being a maximal (left) r-ideal is established. It is shown that (left) r-ideals and (left) k-ideals coincide for an additively idempotent semiring, though the former is a special kind of the latter in general. It is proved that a proper k-ideal of an incline with an identity is a maximal k-ideal if and only if the corresponding congruence class semiring is the Boolean semiring.

scholarly journals ON THE ANNIHILATOR GRAPH OF GROUP RINGS

2017 ◽  
Vol 54 (1) ◽  
pp. 331-342
Author(s):  
Mojgan Afkhami ◽  
Kazem Khashyarmanesh ◽  
Sepideh Salehifar
Keyword(s):  
Group Rings ◽  
Annihilator Graph

Crosscap two of class of graphs from commutative rings

2021 ◽  
Author(s):  
S. Karthik ◽  
S. N. Meera ◽  
K. Selvakumar
Keyword(s):  
Commutative Ring ◽  
Undirected Graph ◽  
Commutative Rings ◽  
Zero Divisors ◽  
Essential Ideal ◽  
Vertex Set ◽  
Annihilator Graph ◽  
Finite Commutative Rings

Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be the set of all nonzero zero-divisors of [Formula: see text]. The annihilator graph of commutative ring [Formula: see text] is the simple undirected graph [Formula: see text] with vertices [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. The essential graph of [Formula: see text] is defined as the graph [Formula: see text] 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] is an essential ideal. In this paper, we classify all finite commutative rings with identity whose annihilator graph and essential graph have crosscap two.

Some Remarks on the Annihilator Graph of a Commutative Ring

2020 ◽  
Vol 49 (2) ◽  
pp. 325-332
Author(s):  
M. ADLIFARD ◽  
Sh. PAYROVI
Keyword(s):  
Commutative Ring ◽  
Annihilator Graph

scholarly journals On strong shift equivalence over a Boolean semiring

1986 ◽  
Vol 6 (1) ◽  
pp. 81-97 ◽  
Author(s):  
Ki Hang Kim ◽  
Fred W. Roush
Keyword(s):  
Equivalence Relation ◽  
Equivalence Classes ◽  
Directed Edge ◽  
Strong Shift ◽  
Shift Equivalence ◽  
Edge Graph ◽  
Boolean Semiring ◽  
Strong Shift Equivalence

AbstractShift equivalence is the relation between A, B that there exists S, R, n > 0 with RA = BR, AS = SB, SR = An, RS = Bn. Strong shift equivalence is the equivalence relation generated by these equations with n = 1. We prove that for many Boolean matrices strong shift equivalence is characterized by shift equivalence and a trace condition. However, we also show that if A is strongly shift equivalent to B, then there exists a homomorphism from an iterated directed edge graph of A to the graph of B preserving the traces of powers. This yields results on colourings of iterated directed edge graphs and might distinguish new strong equivalence classes.

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