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Hamid Kulosman

Publications and source records attributed to Hamid Kulosman.

9 recordsLinked to original sources
arXiv2020

Some properties of pseudomeadows

The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I.~Bethke, P.~Rodenburg, and A.~Sevenster in their 2015 paper, to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as the subdirect products of fields to the case of commutative pseudomeadows. Finally we investigate localizations of commutative pseudomeadows.

math.AC↗
arXiv2020

Some remarks about trunks and morphisms of neural codes

We give intrinsic characterizations of neural rings and homomorphisms between them. Also we introduce the notion of a basic monomial code map and characterize monomial code maps as compositions of basic monomial code maps. Finally, we characterize monomial isomorphisms between neural codes. Our work is based on the 2015 paper by C.~Curto and N.~Youngs about neural ring homomorphisms and maps between neural codes and on the 2018 paper by R.~Amzi Jeffs about morphisms of neural rings.

math.AC↗
arXiv2018

For which additive submonoids $M$ of nonnegative rationals is $F[X;M]$ AP?

We characterize the submonoids $M$ of the additive monoid $\Q_+$ of nonnegative rational numbers for which the irreducible and the prime elements in the monoid domain $F[X;M]$ coincide. We present a diagram of implications between some types of submonoids of $\Q_+$, with a precise position of the monoids $M$ with this property.

math.AC↗
arXiv2018

A new characterization of principal ideal domains

In 2008 N.~Q.~Chinh and P.~H.~Nam characterized principal ideal domains as integral domains that satisfy the follo\-wing two conditions: (i) they are unique factorization domains, and (ii) all maximal ideals in them are principal. We improve their result by giving a characterization in which each of these two conditions is weakened. At the same time we improve a theorem by P.~M.~Cohn which characterizes principal ideal domains as atomic Bézout domains. We will also show that every PC domain is AP and that the notion of PC domains is incomparable with the notion of pre-Schreier domains (hence with the notions of Schreier and GCD domains as well).

math.AC↗
arXiv2018

Polarization of neural codes

The neural rings and ideals as an algebraic tool for analyzing the intrinsic structure of neural codes were introduced by C.~Curto et al. in 2013. Since then they were investigated in several papers, including the 2017 paper by Güntürkün et al., in which the notion of polarization of neural ideals was introduced. In this paper we extend their ideas by introducing the notions of polarization of motifs and neural codes. We show that the notions that we introduced have very nice properties which could allow the studying of the intrinsic structure of neural codes of length $n$ via the square free monomial ideals in $2n$ variables and interpreting the results back in the original neural code ambient space. In the last section of the paper we introduce the notions of inactive neurons, partial neural codes, and partial motifs, as well as the notions of polarization of these codes and motifs. We use these notions to give a new proof of a theorem from the paper by Güntürkün et al. that we mentioned above.

math.AC↗