Artinian ring
On radical square zero rings
... zero ring and S, T are simple R-modules then P T = QS if and only if there is an arrow α : T → S with l(α) = 1 and this is the only arrow starting at T and the only arrow ending in ...left artinian ...
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Prime radical of Ore extensions over \(\delta\)-rigid rings
... right Artinian ring, where δ is a derivation of ...Noetherian ring and σ is an automorphism of R, then the skew-polynomial ring R[x, σ] embeds in an Artinian ...a ring which is ...
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Left localizations of left Artinian rings
... left Artinian ring if it is not stated ...left Artinian ring R, that every left localization of R is an idempotent left localization (Theorem ...
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Graded Essential Extensions and Graded Injective Modules
... noetherian ring or a right artinian ring then there exists a bijection between the set of isomorphism classes of right indecomposable injective R-modules and the set of all prime ideals of R ...
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Analysis of Algebra of Complex Analysis
... A ring that is a semisimple module over itself is known as an Artinian semisimple ...An Artinian ring is at first comprehended by means of its biggest semisimple ...of Artinian ...
15
Generalizations of the theory of quasi frobenius rings
... Since any ring R is generated as a right or a left R-module by 1R' the above theoren shows that a semi-simple Artinian ring can be expressed as a direct sum of a finite number of minimal[r] ...
170
Orders in Artinian rings, Goldie's Theorem and the largest left quotient ring of a ring
... a ring to have a left Artinian left quotient ring that are due to Small (1966), Robson (1967), Tachikawa (1971) and Hajarnavis ...a ring have a semi-simple (Artinian) left quotient ...
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Whitehead groups of exchange rings with primitive factors artinian
... By using Zorn’s lemma, we have a two-sided ideal Q of R such that it is maximal in Ω. Let S = R/Q. If J(R/Q) ≠ 0, then J(R/Q) = K/Q for some K ⊃ Q. Clearly, S/J(S) R/K. By the maximality of Q, we can find a unit-regular ...
6
Some results on a subgraph of the intersection graph of ideals of a commutative ring
... Artinian ring. It is convenient to denote X + J by x and Y + J by y. Observe that m J = Rx + Ry is not principal, xy 6= 0 + J, Rxy ⊂ Rx, and Rxy ⊂ Ry. Therefore, R admits nonzero proper ideals other than ...
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On a Proper Subclass of Primeful Modules Which Contains the Class of Finitely Generated Modules Properly
... (Q : M )/Ann(M) is a surjective map. The class of φ-modules is a proper subclass of primeful modules, called ψ-modules here, and contains the class of finitely generated modules properly. Indeed, φ and ψ are two sides of ...
7
SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS
... to Artinian rings. We will see that an Artinian ring is a ring in which every descending chain of ideals becomes ...an Artinian ring: finiteness and ...
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Positive Implicative Artinian and Positive Implicative Noetherian Hyper Bck Algebras
... Theorem 2.4. Let H be a hyper BCK- algebra. If every intuitionistic fuzzy positive implicative hyper BCK- ideal of type-1of H has finite number of intuitionistic fuzzy values, then H is a PI- Artinian hyper ...
7
Vol 3, No 8 (2012)
... again Artinian Near Ring. If in a commutative Artinian Near Ring N, is a module such that no element of the form 1 + M ...commutative Artinian Near Ring every module has a ...
7
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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On N Fold Positive Implicative Artinian and Positive Implicative Notherian BCK Algebras
... implicative Artinian (shortly, PI n -Artinian) and n-fold positive implicative Noe-therian (shortly, PI n -Noetherian) BCK-algebras and study some of its ...
5
Chain conditions on semirings
... the descending chain condition on left deals [k-ideals, h-Ideals] of S... Obviously, aruman mplies k-artman and the latter mplies h-artinian..[r] ...
6
Effective ring
... b / ∈ J (aR) then by simple observation element r is not a unit in a ring R. Then equality rR + bR = R implies that ru + bv = 1 for some elements u, v ∈ R. Then rsu + bsv = s. Since a = rs then rs = 0 and we have ...
8
On pairs of subrings with a common set of proper ideals
... A ring is called fully idempotent if every ideal of R is idempotent. A ring R is called von Neumann regular provided that for every x ∈ R there exists y ∈ R such that xyx = ...idempotent ring is von ...
8
Nagata rings and directed unions of Artinian subrings
... GF(p)(X) in R. The ring is the biggest subring of R which is a directed union of Artinian subrings. We remark that, if V ⊂ , then, by [11, Corollary 4], V is also a directed union of Artinian ...
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Annihilators of Artinian modules compatible with a Frobenius map
... a ring of formal power series over a field K of prime characteristic p, m will denote its maximal ideal, and E = E R (R/ m ) will denote the injective hull of its residue ...
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