Browsing by Author "Atani, Shahabaddin Ebrahimi"

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    Lattice structures of automata
    (Ankara Üniversitesi Fen Fakültesi, 2020-12-31) Atani, Shahabaddin Ebrahimi; Sedghi Shanbeh Bazari, Maryam; Other; Other
    This paper is motivated by the results in [M. Ito, Algebraic structures of automata, Theoretical Computer Science 428 (2012) 164-168.]. Structures and the number of subautomata of a finite automaton are investigated. It is shown that the set of all subautomata of a finite automaton A is upper semilattice. We give conditions which allow us to determine whether for a finite upper semilattice (L;≤) there exists an automaton A such that the set of all subautomata of A under set inclusion is isomorphic to (L;≤). Examples illustrating the results are presented.
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    On a graph of ideals of a commutative ring
    (Ankara Üniversitesi Fen Fakültesi, 2019-08-01) Khoramdel, Mehdi; Atani, Shahabaddin Ebrahimi; Pishhesari, Saboura Dolati; Other; Other
    In this paper, we introduce and investigate a new graph of a commutative ring R, denoted by G(R), with all nontrivial ideals of R as vertices, and two distinct vertices I and J are adjacent if and only if ann(I∩J)=ann(I)+ann(J). In this article, the basic properties and possible structures of the graph G(R) are studied and investigated as diameter, girth, clique number, cut vertex and domination number. We characterize all rings R for which G(R) is planar, complete and complete r-partite. We show that, if (R,M) is a local Artinian ring, then G(R) is complete if and only if Soc(R) is simple. Also, it is shown that if R is a ring with G(R) is r-regular, then either G(R) is complete or null graph. Moreover, we show that if R is an Artinian ring, then R is a serial ring if and only if G(R/I) is complete for each ideal I of R.