6 papers
On the distributivity of the subtractive closure operator over ideal operations in hemirings
Peyman Nasehpour
In this paper, we investigate the subtractive closure operator in commutative hemiring theory. While this operator satisfies standard closure properties, it does not distribute ove…
Algebraic properties of overflow semirings
Peyman Nasehpour
We introduce the overflow semiring , extending a positive information algebra by a join-semilattice , where elements of dominate …
Hemiring-valued pseudonormed rings
Peyman Nasehpour
In the second section, we introduce hemiring-valued pseudonormed rings and generalize Albert's result which states that every finite-dimensional algebra can be normed. Next, we int…
Algebraic properties of Indigenous semirings
Hussein Behzadipour, Henk Koppelaar, Peyman Nasehpour
In this paper, we introduce Indigenous semirings and show that they are examples of information algebras. We also attribute a graph to them and discuss their diameters, girths, and…
Covering conditions for ideals in semirings
Peyman Nasehpour
In this paper, we prove prime avoidance for ringoids. We also generalize McCoy's and Davis' prime avoidance theorems in the context of semiring theory. Next, we proceed to define a…
Classical semirings
Hussein Behzadipour, Henk Koppelaar, Peyman Nasehpour
In this paper, we investigate semirings whose elements are either units or zero-divisors (nilpotents) with many examples. While comparing these semirings with their counterparts in…