Results 11 to 20 of about 904 (238)
A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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Vector spaces over finite commutative rings [PDF]
19 ...
Jun Guo, Junli Liu, Qiuli Xu
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NeutroAlgebra of Idempotents in Group Rings [PDF]
Neutrosophic Sets and Systems, 2022 In this paper, the authors study the new concept of NeutroAlgebra of idempotents in group rings. It is assumed that RG is the group ring of a group G over the ring R. R should be a commutative ring with unit 1.
Vasantha Kandasamy +1 more
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AIMS Mathematics, 2022 An associative Artinian ring with an identity is a chain ring if its lattice of left (right) ideals forms a unique chain. In this article, we first prove that for every chain ring, there exists a certain finite commutative chain subring which ...
Yousef Alkhamees, Sami Alabiad
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Enumeration of Involutions of Finite Rings
Journal of New Theory, 2021 In this paper, we study a special class of elements in the finite commutative rings called involutions. An involution of a ring R is an element with the property that x^2-1=0 for some x in R.
Sajana Shaık, Chalapathi Tekurı
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The Mathematical Safe Problem and Its Solution (Part 2)
Кібернетика та комп'ютерні технології, 2021 Introduction. The problem of mathematical safe arises in the theory of computer games and cryptographic applications. The article considers numerous variations of the mathematical safe problem and examples of its solution using systems of linear ...
Sergii Kryvyi, Hryhorii Hoherchak
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Random Motion on Finite Rings, I: Commutative Rings [PDF]
Algebras and Representation Theory, 2019 We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first prove formulas for eigenvalues and multiplicities of the transition matrices of these chains using the character ...
Arvind Ayyer, Pooja Singla
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On classification of finite commutative chain rings
AIMS Mathematics, 2022 Let $ R $ be a finite commutative chain ring with invariants $ p, n, r, k, m. $ It is known that $ R $ is an extension over a Galois ring $ GR(p^n, r) $ by an Eisenstein polynomial of some degree $ k $.
Sami Alabiad, Yousef Alkhamees
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Nonisotropic symplectic graphs over finite commutative rings
AIMS Mathematics, 2022 In this paper, we study two types of nonisotropic symplectic graphs over finite commutative rings defined by nonisotropic free submodules of rank 2 and McCoy rank of matrices. We prove that the graphs are quasi-strongly regular or Deza graphs and we find
Songpon Sriwongsa, Siripong Sirisuk
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Computation of eccentric topological indices of zero-divisor graphs based on their edges
AIMS Mathematics, 2022 The topological index of a graph gives its topological property that remains invariant up to graph automorphism. The topological indices which are based on the eccentricity of a chemical graph are molecular descriptors that remain constant in the whole ...
Ali N. A. Koam +3 more
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