14 citations · 123 across the 26 of their papers we have counts for
27 papers
Magma-valued metric spaces
Peyman Nasehpour
In the second section, we introduce dense unital magmas and show that a near-ring is dense if and only if it has a positive element smaller that unity. In the third section, we dis…
Amount algebras
Peyman Nasehpour
In this paper, as a generalization to content algebras, we introduce amount algebras. Similar to the Anderson-Badawi conjecture, we prove that under some co…
On Hardy's Apology Numbers
Henk Koppelaar, Peyman Nasehpour
Twelve well known `Recreational' numbers are generalized and classified in three generalized types Hardy, Dudeney, and Wells. A novel proof method to limit the search for the numbe…
A generalization of zero-divisor graphs
Peyman Nasehpour
In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate thei…
Dedekind semidomains
Peyman Nasehpour
We define Dedekind semidomains as semirings in which each nonzero fractional ideal is invertible. Then we find some equivalent condition for semirings to being Dedekind. For exampl…
Gauss' lemma for polynomials over semidomains
Peyman Nasehpour
In this paper, we generalize Gauss' lemma for polynomials over subtractive factorial semidomains.
Eversible and reversible semigroups and semirings
Peyman Nasehpour
The main purpose of this paper is to investigate the zero-divisors of semigroups with zero and semirings and in particular, to discuss eversible and reversible semigroups and semir…
Algebraic properties of expectation semirings
Peyman Nasehpour
In this paper, we investigate the algebraic properties of the expectation semirings which are semiring version of the concept of trivial extension in ring theory. We discuss ideals…
Distinguished elements in semiring extensions
Peyman Nasehpour
In this paper, we investigate zero-divisor, nilpotent, idempotent, unit, small, and irreducible elements in semiring extensions such as amount, content, and monoid semialgebras. We…
Some remarks on the comparability of ideals in semirings
H. Behzadipour, P. Nasehpour
A semiring is uniserial if its ideals are totally ordered by inclusion. First, we show that a semiring is uniserial if and only if the matrix semiring is uniserial. As…
A Brief History of Algebra with a Focus on the Distributive Law and Semiring Theory
Peyman Nasehpour
In this note, we investigate the history of algebra briefly. We particularly focus on the history of rings, semirings, and the distributive law.
Some Remarks on Ideals of Commutative Semirings
Peyman Nasehpour
The main purpose of this paper is to investigate prime, primary, and maximal ideals of semirings. The localization and primary decomposition of ideals in semirings are also studied…
On 2-absorbing ideals of commutative semirings
Hussein Behzadipour, Peyman Nasehpour
In this paper, we investigate 2-absorbing ideals of commutative semirings and prove that if is a nonzero proper ideal of a subtractive valuation semiring then $\…
Some remarks on semirings and their ideals
Peyman Nasehpour
In this paper, we give semiring version of some classical results in commutative algebra related to Euclidean rings, PIDs, UFDs, G-domains, and GCD and integrally closed domains.
On graphs of bounded semilattices
Parastoo Malakooti Rad, Peyman Nasehpour
In this paper, we introduce the graph of a bounded semilattice , which is a generalization of the intersection graph of the substructures of an algebraic structure. We pr…
Auslander Modules
Peyman Nasehpour
In this paper, we introduce the notion of Auslander modules, inspired from Auslander's zero-divisor conjecture (theorem) and give some interesting results for these modules. We als…
Pseudocomplementation and Minimal Prime Ideals in Semirings
Peyman Nasehpour
In the first section of the present work, we introduce the concept of pseudocomplementation for semirings and show semiring version of some known results in lattice theory. We also…
On zero-divisors of semimodules and semialgebras
Peyman Nasehpour
In Section 1 of the paper, we prove McCoy's property for the zero-divisors of polynomials in semirings. We also investigate zero-divisors of semimodules and prove that under suitab…
Finitely Additive, Modular and Probability Functions on Pre-semirings
Peyman Nasehpour, Amir Hossein Parvardi
In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemente…
Valuation Semirings
Peyman Nasehpour
The main scope of this paper is to introduce valuation semirings in general and discrete valuation semirings in particular. In order to do that, first we define valuation maps and…
Invertible Ideals and Gaussian Semirings
Shaban Ghalandarzadeh, Peyman Nasehpour, Rafieh Razavi
In the first section of this paper, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we…
On the Anderson-Badawi conjecture
Peyman Nasehpour
Let be a commutative ring with an identity different from zero and be a positive integer. Anderson and Badawi, in their paper on -absorbing ideals, define a proper ideal…
On the Content of Polynomials Over Semirings and Its Applications
Peyman Nasehpour
In this paper, we prove that Dedekind-Mertens lemma holds only for those semimodules whose subsemimodules are subtractive. We introduce Gaussian semirings and prove that bounded di…
Zero-divisor graphs of nilpotent-free semigroups
Neil Epstein, Peyman Nasehpour
We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an \emph{Armendariz map} betwee…