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Principal ideal ring

A class of principal ideal rings arising from the converse of the
Chinese remainder theorem

A class of principal ideal rings arising from the converse of the Chinese remainder theorem

... a ring R, then the canonical ring homomorphism R/(I ∩ J) → R/I × R/J, given by r + I ∩ J → (r + I,r + J), is an isomorphism if and only if I + J = R ...(unspecified) ring isomorphism between R/ ( I ∩ ...

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Artinian rings, finite principal ideal rings and algebraic error correcting codes

Artinian rings, finite principal ideal rings and algebraic error correcting codes

... Chapter 4 : Radicals of finite rings and principal ideal rings In Chapter 4 several necessary and sufficient conditions are given which characterize radical semisimple, radical and semis[r] ...

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Non Noetherian unique factorisation rings

Non Noetherian unique factorisation rings

... all principal. We also show that if T is a reflexive ideal o f R then R /T has a quotient ring which is an Artinian principal ideal ...

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A Graphical Characterization for SPAP-Rings

A Graphical Characterization for SPAP-Rings

... a ring has the property that every ideal is a product of prime ideals if and only if it is a finite direct product of Dedekind domains and special principal ideal rings (SP IRs)(For more ...

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SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS

... a ring having no nonzero nilpotent ideals and suppose Re is a minimal left ideal of R with e being ...a ring with unity ...division ring, consider a nonzero element eae ∈ ...a principal ...

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Structure of weakly periodic rings with potent extended commutators

Structure of weakly periodic rings with potent extended commutators

... a ring R with the property that, for each x in R, there exists an integer n(x) > 1 such that x n(x) = x is necessarily ...periodic ring R with a “sufficient” number of potent extended commutators. A ...

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A radical for right near rings: The right Jacobson radical of
type 0

A radical for right near rings: The right Jacobson radical of type 0

... an ideal of ...prime ideal of R by Theorem ...(left) ideal K and is right (left) modular by the ...largest ideal of R contained in ...0-primitive ideal of R and ...

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Hanoi Zariski complete

Hanoi Zariski complete

... Proof. As R/m is infinite, we may pick x, y ∈ m so that m = (x, y) and I and J are contracted from S = R[y/x]. Assume for a moment that Im : x = I and Jm : x = J. Then Im : x = I = mJ : x = J. To show that Im : x = I, ...

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A generalization of a theorem of Faith and Menal and applications

A generalization of a theorem of Faith and Menal and applications

... A ring R is called a right V-ring if R is a V-module when considered as a right module over itself, ...the ring theory we mainly follow Anderson and Fuller [2] and Wisbauer ...

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Semi-Prime Ideals of Gamma Rings

Semi-Prime Ideals of Gamma Rings

... two-sided) ideal, called the sum of A and ...two-sided) ideal of a Γ-ring is also a left (respectively right or two-sided) ...sided) ideal of M is also a left (respectively right or two-sided) ...

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Some Notes on Semiabelian Rings

Some Notes on Semiabelian Rings

... a ring R idempotent reversible if gRe 0 implies eRg 0 for e, g ∈ ...a ring R is left idempotent reflexive if and only if for any a ∈ NR, aRe 0 implies eRa ...

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Classical quotient rings of generalized matrix rings

Classical quotient rings of generalized matrix rings

... So, if R is a generalized matrix ring with idempotent set E and e, f e E with e f, then ZeRe is the right singular ideal of the ring eRe and ZeRfis the right singular submodule of the ri[r] ...

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On Completely And Semi Completely Prime Ideal With Respect To An Element Of A Boolean 1, 2 Near-Ring

On Completely And Semi Completely Prime Ideal With Respect To An Element Of A Boolean 1, 2 Near-Ring

... near- ring and later 1930 Wieland has investigated it ...near ring can be found ...prime ideal with respect to an element of a near-ring[4] ...

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Security  Analysis  of  Cryptosystems  Using  Short  Generators  over  Ideal  Lattices

Security Analysis of Cryptosystems Using Short Generators over Ideal Lattices

... the principal ideal (g), such as the Hermite normal form HNF(g), is used as a public key ...a Principal Ideal Problem, SG-PIP) Let K be a number field and O K its ring of ...

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On n flat modules and n Von Neumann regular rings

On n flat modules and n Von Neumann regular rings

... We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n − 1)-ring (resp., a weakly (n,n − 1)-ring). We also give a new characterization of n-von Neumann regular rings and a ...

6

Right orders in full linear rings

Right orders in full linear rings

... with zero right singular ideal, but not an integral domain, if S contains uniform right ideals then S 1s a right quotient ring of any prime ring over which it 1s right... This result has[r] ...

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A result of commutativity of rings

A result of commutativity of rings

... If there exists no prime p for which the ring of 2 x 2 matrices over GFp satisfies qX 0, then R has a nil commutator ideal and the nilpotent elements of R form an ideal... If for some po[r] ...

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Bipolar-Valued Fuzzy Ideals of Ring and Bipolar-Valued Fuzzy Ideal Extensions in Subrings

Bipolar-Valued Fuzzy Ideals of Ring and Bipolar-Valued Fuzzy Ideal Extensions in Subrings

... 𝛼 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 is a fuzzy ideal” from this 𝑃 is clearly a non-constant fuzzy ideal. Let 𝐴 and 𝐵 be any fuzzy ideals and let 𝐴 ≤ 𝑃, 𝐵 ≤ 𝑃. Then there exist 𝑥, 𝑦 in 𝑅, such that 𝐴 𝑥 ≮ 𝑃 𝑥 , 𝐵 𝑥 ≰ 𝑃 𝑥 . This ...

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Generalized Baer rings

Generalized Baer rings

... A ring satisfying a generalization of Rickart’s condition ...right ideal) by an idempotent) has a homological charac- terization as a right PP-ring which is also another generalization of a Baer ...A ...

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Characterizing the strong two-generators of certain Noetherian domains

Characterizing the strong two-generators of certain Noetherian domains

... Next we show that in a Noetherian ring these three properties are equivalent: that any ideal in the ring is finitely generated, that every nonempty set of ideals contains a maximal el[r] ...

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