Yazd UniversityAlgebraic Structures and Their Applications2382-97613120160201HX-hypergroups associated with the direct products of some ${\bf Z}/n {\bf Z}$115835ENPiergiulioCorsiniUniversity of Udine, ItalyJournal Article20161026One studies the $HX$-hypergroups, corresponding to the Chinese hypergroups associated with the direct products of some ${\bf Z}/n {\bf Z},$ calculating their fuzzy grades.Yazd UniversityAlgebraic Structures and Their Applications2382-97613120160201A note on the order graph of a group1724875ENHamid RezaDorbidiUniversity of JiroftJournal Article20150430 The order graph of a group $G$, denoted by $\Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|\big{|}|K|$ or $|K|\big{|}|H|$.<br /> In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.Yazd UniversityAlgebraic Structures and Their Applications2382-97613120160201Exact sequences of extended $d$-homology2538886ENMohammad ZaherKazemi BanehUniversity of KurdistanSeyed NaserHosseiniShahid Bahonar University of KermanJournal Article20161018In this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. We present sufficient conditions for the existence of long exact extended d- homology sequence. Also we give some illustrative examples.Yazd UniversityAlgebraic Structures and Their Applications2382-97613120160201The principal ideal subgraph of the annihilating-ideal graph of commutative rings3952888ENRezaTaheriIslamic Azad University, Science and Research Branch, Tehran, IranAbolfazlTehranianIslamic Azad University, Science and Research Branch, Tehran, IranJournal Article20150928Let $R$ be a commutative ring with identity and $\mathbb{A}(R)$ be the set of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $\mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $\mathbb{A}_P(R)=\mathbb{A}(R)\cap \mathbb{P}(R)\setminus \{(0)\}$, where $\mathbb{P}(R)$ is the set of proper principal ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=(0)$. Then, we study some basic properties of $\mathbb{AG}_P(R)$. For instance, we characterize rings for which $\mathbb{AG}_P(R)$ is finite graph, complete graph, bipartite graph or star graph. Also, we study diameter and girth of $\mathbb{AG}_P(R)$. Finally, we compare the principal ideal subgraph $\mathbb{AG}_P(R)$ and spectrum subgraph $\mathbb{AG}_s(R)$.Yazd UniversityAlgebraic Structures and Their Applications2382-97613120160201The concept of logic entropy on D-posets5361900ENUosefMohammadiUniversity of JiroftJournal Article20160405In this paper, a new invariant called {\it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {\it conditional logical entropy} is defined and then some of its properties are studied. The invariance of the {\it logic entropy} of a system under isomorphism is proved. At the end, the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolmogorov-Sinai theorem is given.