Yazar "Babaei, Sakineh" seçeneğine göre listele

Listeleniyor 1 - 3 / 3
  • Küçük Resim Yok
    Öğe
    A Submodule-Based Zero Divisor Graph for Modules
    (Tarbiat Modares Univ, 2019) Babaei, Sakineh; Payrovi, Shiroyeh; Sevim, Esra Sengelen
    Let R be a commutative ring with identity and M be an R-module. The zero divisor graph of M is denoted by Gamma(M). In this study, we are going to generalize the zero divisor graph Gamma(M) to submodule-based zero divisor graph Gamma(M, N) by replacing elements whose product is zero with elements whose product is in some submodule N of M. The main objective of this paper is to study the interplay of the properties of submodule N and the properties of Gamma(M, N).
  • Küçük Resim Yok
    Öğe
    On the Annihilator Submodules and the Annihilator Essential Graph
    (Springer Singapore Pte Ltd, 2019) Babaei, Sakineh; Payrovi, Shiroyeh; Sevim, Esra Sengelen
    Let R be a commutative ring and let M be an R-module. For a is an element of R, Ann(M)(a) = {m is an element of M : am = 0} is said to be an annihilator submodule of M. In this paper, we study the property of being prime or essential for annihilator submodules of M. Also, we introduce the annihilator essential graph of equivalence classes of zero divisors of M, AE(R)(M), which is constructed from classes of zero divisors, determined by annihilator submodules of M and distinct vertices [a] and [b] are adjacent whenever Ann(M)(a) + Ann(M)(b) is an essential submodule of M. Among other things, we determine when AE(R)(M) is a connected graph, a star graph, or a complete graph. We compare the clique number of AE(R)(M) and the cardinal of m -Ass(R)(M).
  • Küçük Resim Yok
    Öğe
    On the compressed essential graph of a commutative ring
    (Belgian Mathematical Soc Triomphe, 2019) Payrovi, Shiroyeh; Babaei, Sakineh; Sevim, Esra Sengelen
    Let R be a commutative ring. In this paper, we introduce and study the compressed essential graph of R, EG(E)(R). The compressed essential graph of R is a graph whose vertices are equivalence classes of non-zero zero-divisors of R and two distinct vertices [x] and [y] are adjacent if and only if ann(xy) is an essential ideal of R. It is shown if R is reduced, then EG(E)(R) = Gamma(E)(R), where Gamma(E)(R) denotes the compressed zero-divisor graph of R. Furthermore, for a non-reduced Noetherian ring R with 3 < vertical bar EG(E)(R)vertical bar < infinity, it is shown that EG(E)(R) = Gamma(E)(R) if and only if (i) Nil(R) = ann(Z(R)). (ii) Every non-zero element of Nil(R) is irreducible in Z(R).