[PDF] Top 20 Number theoretic properties of the commutative ring Zn

... the properties of counting ...deep properties of ...of number theory, in particular the notion of congruence of numbers in graph theory and motivated the special way for emerging of a new class of ... See full document

... a number of papers in which the graphs associated to rings were introduced and their properties ...a ring , the set of vertices is taken to be and two vertices x and y are adjacent if and only if xy ... See full document

... We review some basic graph-theoretic definitions, and for the necessary definitions and notations of hypergraphs, we refer the reader to standard texts of graph theory such as [10]. A hypergraph is a pair (V ,E) ... See full document

... are commutative with ...a ring and investigated the interplay between the ring-theoretic properties of a ring and the graph- theoretic properties of the graph ... See full document

... arbitrary ring F; and together with the operations of rhotrix addition ‘+’ and row-column based method for rhotrix multiplication; ' ' , so as to introduce it as “the concept of non-commutative full rhotrix ... See full document

... of ring and initiated the study of the relation between ring- theoretic properties and graph theoretic ...of commutative rings have attracted the attention of several researchers ... See full document

... are commutative rings with identity 1 6= ...of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic ... See full document

... a commutative ring was introduced in [14], by studying the coloring of a graph constructed by all elements of a commutative ring ...the ring-theoretic properties of a ... See full document

... If ( X, ∗ , e ) is a group which is pseudo-commutative, then e = x ∗ x −1 = ξ ( x −1 ) ∗ ξ ( x ) for some ϕ : X → X, so that ξ ( x ) −1 = ξ ( x −1 ) . Hence ( ξ ( e )) −1 = ξ ( e −1 ) = ξ ( e ) . Since x = x ∗ e = ... See full document

... 3.2. The comonad U for K-theory. The discussion in this section closely follows Boardman et al. [4, Section 8], except that we take into account the periodicity of K-theory and consider only the degree-0 part. We first ... See full document

... Experimental study of heat capacity of Zn- 5Al and Zn-55Al alloy with Magnesium were carried out by cooling method, according to Newton law. Anything with a temperature above the ambient temperature will Mg ... See full document

... are commutative with identity which admit at least one nonzero proper ...a ring with identity which is not necessar- ily commutative and which admits at least one nonzero left ideal I with I 6= ... See full document

... A ring is called semi primitive or Jacobson semi basic if its Jacobson radical is the zero ...A ring is semi primitive if and just on the off chance that it has an unwavering semi straightforward left ...a ... See full document

... In [4], M. F. Hoque and A.C Paul have proved that if M is a 2-torsion free semiprime Γ -ring satisfying the assumption (A) and if T : M → M is an additive mapping such that T ( x α y β x ) = x α T ( y ) β x for ... See full document

... by Krull’s Intersection Theorem. Now the proof is complete. Corollary 5.3. Suppose that (R, m) is a formally catenary local ring all of whose for- mal fibres are Cohen–Macaulay. (These hypotheses would be ... See full document

... In this section we give an example of the use the Hartshorne–Speiser–Lyubeznik Theorem to obtain a result, of the type mentioned in the Introduction, about uniform behaviour of Frobenius closures in a Cohen–Macaulay ... See full document

... Introduction: One of the most important functions in number theory is the Euler function ∅(𝒏) first introduced by Euler. Euler (1707 – 1783), is universally considered as one of the greatest mathematicians in ... See full document

... Proof. The proof is an immediate consequence of Theorems 6 and 4. Corollary 8. Let R be a noncommutative prime ring of characteristic di ff erent from two. Suppose that there exist a derivation D : R → R and an ... See full document

... in commutative algebra of Noe- therian rings, namely those associated to Gorenstein local ...For ring spectra there is a corresponding development, starting by restricting the class of rings by a finiteness ... See full document

... The study of projective and injective modules constitutes the backbone of the modern homological algebra. Injective modules are closely related to essential extensions. Actually, if R is an associative ring with 1 ... See full document