On the Annihilator Submodules and the Annihilator Essential Graph
Küçük Resim Yok
Tarih
2019
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Singapore Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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).
Açıklama
Anahtar Kelimeler
Annihilator Submodule, Annihilator Essential Graph, Zero Divisor Graph, Zero-Divisor Graph
Kaynak
Acta Mathematica Vietnamica
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
44
Sayı
4
