z0-Ideals and some special commutative rings
نویسندگان
چکیده
منابع مشابه
Generalizations of Primary Ideals in Commutative Rings
Let R be a commutative ring with identity. Let φ : I(R) → I(R) ∪ {∅} be a function where I(R) denotes the set of all ideals of R. A proper ideal Q of R is called φ-primary if whenever a, b ∈ R, ab ∈ Q−φ(Q) implies that either a ∈ Q or b ∈ √ Q. So if we take φ∅(Q) = ∅ (resp., φ0(Q) = 0), a φ-primary ideal is primary (resp., weakly primary). In this paper we study the properties of several genera...
متن کاملT -rough Semiprime Ideals on Commutative Rings
Rough sets were originally proposed in the presence of an equivalence relation. An equivalence relation is sometimes difficult to be obtained in rearward problems due to the vagueness and incompleteness of human knowledge. The purpose of this paper is to introduce and discuss the concept of T -rough semiprime ideal, T -rough fuzzy semiprime ideal and T -rough quotient ideal in a commutative rin...
متن کاملSome Properties of the Nil-Graphs of Ideals of Commutative Rings
Let R be a commutative ring with identity and Nil(R) be the set of nilpotent elements of R. The nil-graph of ideals of R is defined as the graph AG_N(R) whose vertex set is {I:(0)and there exists a non-trivial ideal such that and two distinct vertices and are adjacent if and only if . Here, we study conditions under which is complete or bipartite. Also, the independence number of is deter...
متن کاملGraphs and principal ideals of finite commutative rings
In [1], Afkhami and Khashyarmanesh introduced the cozero-divisor graph of a ring, Γ′(R), which examines relationships between principal ideals. We continue investigating the algebraic implications of the graph by developing the reduced cozero-divisor graph, which is a simpler analog. Acknowledgements: This research was undertaken at the Wabash College Mathematics REU in Crawfordsville, Indiana....
متن کاملPRIME IDEALS OF q-COMMUTATIVE POWER SERIES RINGS
We study the “q-commutative” power series ring R := kq[[x1, . . . , xn]], defined by the relations xixj = qijxjxi, for mulitiplicatively antisymmetric scalars qij in a field k. Our results provide a detailed account of prime ideal structure for a class of noncommutative, complete, local, noetherian domains having arbitrarily high (but finite) Krull, global, and classical Krull dimension. In par...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2006
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm189-2-1