Papers by Peyman Nasehpour
Danesh-va-Omid, 2023
درباره زندگی استاد نصرالله ناصحپور که پوینده خلاق راه استاد عبدالله دوامی بود.
international symposium on algorithms and computation, Nov 30, 2017
Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is ... more Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a binary tree can be determined. We present the algorithm BT-leaf, a novel one, to detect the leaf (leaves) of a binary tree from its preorder and postorder traversals in quadratic time and linear space.
international symposium on algorithms and computation, Dec 8, 2016
A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph P n (... more A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph P n (α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles. In this paper we determine a good upper bound for tenacity of cycle permutation graphs.
Journal of Algebraic Combinatorics, 2012
We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nil... more We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an Armendariz map between such semigroups, which preserves many graph-theoretic invariants. We use it to give relationships between the zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal graph. Then we give relationships between the zero-divisor graphs of certain topological spaces (so-called pearled spaces), prime spectra, maximal spectra, tensor-product semigroups, and the semigroup of ideals under addition, obtaining surprisingly strong structure theorems relating ring-theoretic and topological properties to graph-theoretic invariants of the corresponding graphs. Contents 15 7. Prime spectra, maximal spectra, and Alex R 17 8. Application to tensor-product semigroups 19 9. Application to the comaximal ideal graph 20 References 21
Asian-European Journal of Mathematics
A semiring is uniserial if its ideals are totally ordered by inclusion. First, we show that a sem... more A semiring is uniserial if its ideals are totally ordered by inclusion. First, we show that a semiring S is uniserial if and only if the matrix semiring M n (S) is uniserial. As a generalization of valuation semirings, we also investigate those semirings whose prime ideals are linearly ordered by inclusion. For example, we prove that the prime ideals of a commutative semiring S are linearly ordered if and only if for each x, y ∈ S, there is a positive integer n such that either x|y n or y|x n. Then, we introduce and characterize pseudo-valuation semidomains. It is shown that prime ideals of pseudo-valuation semidomains and also of the divided ones are linearly ordered.
Let R be a commutative ring with an identity different from zero and n be a positive integer. And... more Let R be a commutative ring with an identity different from zero and n be a positive integer. Anderson and Badawi, in their paper on n-absorbing ideals, define a proper ideal I of a commutative ring R to be an n-absorbing ideal of R, if whenever x1 . . . xn+1 ∈ I for x1, . . . , xn+1 ∈ R, then there are n of the xi’s whose product is in I and conjecture that ωR[X](I[X]) = ωR(I) for any ideal I of an arbitrary ring R, where ωR(I) = min{n : I is an n-absorbing ideal of R}. In the present paper, we use content formula techniques to prove that their conjecture is true, if one of the following conditions hold: (1) The ring R is a Prüfer domain. (2) The ring R is a Gaussian ring such that its additive group is torsion-free. (3) The additive group of the ring R is torsion-free and I is a radical ideal of R.
Journal of Algebra and Its Applications
In this paper, as a generalization to content algebras, we introduce amount algebras. Similar to ... more In this paper, as a generalization to content algebras, we introduce amount algebras. Similar to the Anderson–Badawi [Formula: see text] conjecture, we prove that under some conditions, the formula [Formula: see text] holds for some amount [Formula: see text]-algebras [Formula: see text] and some ideals [Formula: see text] of [Formula: see text], where [Formula: see text] is the smallest positive integer [Formula: see text] that the ideal [Formula: see text] of [Formula: see text] is [Formula: see text]-absorbing. A corollary to the mentioned formula is that if, for example, [Formula: see text] is a Prüfer domain or a torsion-free valuation ring and [Formula: see text] is a radical ideal of [Formula: see text], then [Formula: see text].
Asian-European Journal of Mathematics
The main purpose of this paper is to investigate the zero-divisors of semigroups with zero and se... more The main purpose of this paper is to investigate the zero-divisors of semigroups with zero and semirings. In particular, we discuss eversible and reversible semigroups and semirings. We also introduce a new ring-like algebraic structure called prenearsemiring and generalize Cohn’s theorem for reversible rings in this context. Finally, we discuss when expectation semirings are reversible or eversible.
Journal of Algebra and Its Applications
In this paper, we investigate 2-absorbing ideals of commutative semirings and prove that if [Form... more In this paper, we investigate 2-absorbing ideals of commutative semirings and prove that if [Formula: see text] is a nonzero proper ideal of a subtractive valuation semiring [Formula: see text] then [Formula: see text] is a 2-absorbing ideal of [Formula: see text] if and only if [Formula: see text] or [Formula: see text] where [Formula: see text] is a prime ideal of [Formula: see text]. We also show that each 2-absorbing ideal of a subtractive semiring [Formula: see text] is prime if and only if the prime ideals of [Formula: see text] are comparable and if [Formula: see text] is a minimal prime over a 2-absorbing ideal [Formula: see text], then [Formula: see text], where [Formula: see text] is the unique maximal ideal of [Formula: see text].
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Journal of Algebra and Its Applications, 2017
The main scope of this paper is to introduce the valuation semirings in general and discrete valu... more The main scope of this paper is to introduce the valuation semirings in general and discrete valuation semirings in particular. In order to do that, first, we define valuation maps and investigate them. Then we define valuation semirings with the help of valuation maps and prove that a multiplicatively cancellative semiring is a valuation semiring if and only if its ideals are totally ordered by inclusion. We also prove that if the unique maximal ideal of a valuation semiring is subtractive, then it is integrally closed. We end this paper by introducing discrete valuation semirings and show that a semiring is a discrete valuation semiring if and only if it is a multiplicatively cancellative principal ideal semiring possessing a nonzero unique maximal ideal. We also prove that a discrete valuation semiring is a Gaussian semiring if and only if its unique maximal ideal is subtractive.
Kyungpook Mathematical Journal
Second Seminar on Algebra and its Applications
In this talk, we prove that in content extensions minimal primes extend to minimal primes and dis... more In this talk, we prove that in content extensions minimal primes extend to minimal primes and discuss zero-divisors of a content algebra over a ring who has Property (A) or whose set of zero-divisors is a finite union of prime ideals. We also examine the preservation of diameter of zero-divisor graph under content extensions.
Kyungpook Math. J, 2000
Let R be a commutative ring with identity. An ideal a of R is called a cancellation ideal if when... more Let R be a commutative ring with identity. An ideal a of R is called a cancellation ideal if whenever ab= ac for ideals b and c of R, then b= c. A good introduction to cancellation ideals may be found in Gilmer [[3]; section 6]. An R–module M is called cancellation module, if whenever aM= bM for ideals a and b of R, then a= b, cf.[6]. The ideal a of R is called an M-cancellation ideal if whenever aP= aQ for submodules P and Q of M, then P= Q. In the first section we characterize M-cancellation ideals. Let M be a cancellation module and let a ...
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Papers by Peyman Nasehpour