Jordan τ-derivations of Prime Rings

Let R be a prime ring which is not commutative, with maximal symmetric ring of quotients Q _ms (R), and let τ be an anti-automorphism of R. An additive map δ: R → Q _ms (R) is called a Jordan τ-derivation if δ(x ²) = δ(x)x ^τ + xδ(x) for all x ∈ R. A Jordan τ-derivation of R is called X-inner if it is of the form x → ax ^τ ? xa for x ∈ R, where a ∈ Q _ms (R). It is proved that any Jordan τ-derivation of R is X-inner if either R is not a GPI-ring or R is a PI-ring except when charR = 2 and dim  _C RC = 4, where C is the extended centroid of R.     

Triangular Matrix Representations of Rings of Generalized Power Series

Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either （S,≤） satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].     

Notes on Jordan (σ, τ)*-derivations and Jordan triple (σ, τ)*-derivations

Let R be a 2-torsion free semiprime *-ring, σ, τ two epimorphisms of R and f, d : R → R two additive mappings. In this paper we prove the following results: (i) d is a Jordan (σ, τ)*-derivation if and only if d is a Jordan triple (σ, τ)*-derivation. (ii) f is a generalized Jordan (σ, τ)*-derivation if and only if f is a generalized Jordan triple (σ, τ)*-derivation.     

Jordan Canonical Form of a Matrix over the Quaternion Field

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On Generalized Jordan Triple (α, β)*-Derivations and Related Mappings

Let R be a 2-torsion free semiprime *-ring and let α, β be surjective endomorphisms of R. The aim of the paper is to show that every generalized Jordan triple (α, β)*-derivation on R is a generalized Jordan (α, β)*-derivation. This result makes it possible to prove that every generalized Jordan triple (α, β)*-derivation on a semisimple H*- algebra is a generalized Jordan (α, β)*-derivation. Finally, we prove that every Jordan triple left α*-centralizer on a 2-torsion free semiprime ring is a Jordan left α*-centralizer.     

A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications

We consider the system of four linear matrix equations A1X = C1, XB2=C2, A3XB3=C3 and A4XB4 = C4 over h, an arbitrary von Neumann regular ring with identity. A necessary and sufficient condition for the existence and the expression of the general solution to the system are derived. As applications, necessary and sufficient conditions are given for the system of matrix equations A1X = C1 and A3X=C3 to have a bisymmetric solution, the system of matrix equations A1X = C1 and A3XB3 = C3 to have a perselfconjugate solution over h with an involution and char h≠2, respectively. The representations of such solutions are also presented. Moreover, some auxiliary resultson other systems over h are obtained. The previous known results on some systems of matrix equations are special cases of the new results.     

Analysis of τ-mesons

We describe in this paper measurements made on the decay products of 11 τ-mesons observed in large nuclear emulsion block detectors. Out of the 33 charged decay products; 27 have been arrested in the block, and were identified as π-mesons. The charge of the τ-meson was found to be positive in 6 cases. In one case the charge of the τ-meson is possibly negative and in 4 cases it could not be determined. Omitting one τ-meson in which a high energy γ-ray is emitted and which has been reported earlier¹ the weighted mean Q-value of the remaining 10 τ-mesons is:

$$Q_\tau = 76 \cdot 3 \pm 0 \cdot 3 MeV$$     

Excellent Extensions of Rings

Ｅｘｃｅｌｌｅｎｔ　Ｅｘｔｅｎｓｉｏｎｓ　ｏｆ　ＲｉｎｇｓＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）ａｎｄＷａｎｇＴｉｎｇＺｈｅｎ（王廷桢）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｃｍａｔｉｃｓ，ＮｏｒｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｎ，７...     

On the Left Classical Quotient Rings of the Superprime Rings

ＯｎｔｈｅＬｅｆｔＣｌａｓｓｉｃａｌＱｕｏｔｉｅｎｔＲｉｎｇｓｏｆｔｈｅＳｕｐｅｒｐｒｉｍｅＲｉｎｇｓＣｈｅｎＰｅｉｃｉ（陈培慈）（Ｄｅｐｔ．ｏｆＭａｔｈ．ＪｉａｎｇｘｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｃｈａｎｇ，ＪｉａｎｇｘｉＰｏｒｖｉｎｃ...     

Implementation of the τ-value

We present a finite noncooperative game in extensive form whose subgame perfect Nash equilibria implement the τ-value.     

Cotorsion Pairs and Stable Categories over Triangular Matrix Rings北大核心CSCD

In general, the properties of modules over a triangular matrix ring T = (0ABU) are studied via modules over diagonal “small rings” A and B. However, we use model structures on the category of T-modules to characterize the stable categories GP(A), GP(B) of Gorenstein projective modules over A and B. To this end, we introduce two subcategories of Gorenstein T-modules, and obtain two corresponding complete cotorsion pairs. Moreover, cotorsion pairs of modules are lifted to T-complexes, and the equivalences and recollements of homotopy categories of complexes are studied. © 2022 Chinese Academy of Sciences. All rights reserved.     

On Decompositions of Quasi-Regular Rings

ＯｎＤｅｃｏｍｐｏｓｉｔｉｏｎｓｏｆＱｕａｓｉ－ＲｅｇｕｌａｒＲｉｎｇｓ￥ＨｕＸｉａｎｈｕｉ（胡先惠）（ＤｅｐａｒｔｍｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｅｎｔｒａｌＩｎｓｔｉｔｕｔｅｏｆＮａｔｉｏｎａｌｉｔｉｅｓ，Ｂｅｉｊｉｎｇ，１０００８１）...     

Results on Commutativity of Rings

We establish two theorems on the commutativity of rings with identity.Whileour first result is based on an iteration method,the second deals with centralconditions.     

Characterizations of Strongly Regular Rings

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＳｔｒｏｎｇｌｙＲｅｇｕｌａｒＲｉｎｇｓＺｈａｎｇＪｕｌｅ（章聚乐）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈｕ２４１０００）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉ...     

Structure of Two-Groups Associative Rings

Introduction.T.S.Ravisanker and U.S.Shukla [1] introduced the notion of a Weak ring A, more general than a ring and a ring in the sense of Nobusawa, and obtained analogical characterizations of the Jacobson radical for weak rings. It is clear that every ring A is a weak ring A for some abelian group (Theorem 3.1 in [2]. Therefore auther gives consideration to such a fact that A and are equal in the weak ring, moreover there is     

Maximal Quotient Rings of Endomorphisms of Quasigenerators

O.Preliminaries. Let R be an associative ring with identity, and let Mod-R denote the category of all unital right R-modules. A set of right ideal of R is called a Gabriel topology on R if satisfies T1. If I∈ and I J, then J∈. T2. If I and J belong to, then I∩J∈. T3. I∈ and r∈R, then (I:r)={x∈R:rx∈I}∈. T4. If I is a right ideal of R and there exists J∈ such that (I:r)∈ for every r∈J, then I∈.     

An axiomatization of the τ-value

The τ-value is characterized by three axioms. It is shown that the τ-value is the unique solution concept which is efficient and has the minimal right property and the restricted proportionality property. The minimal right property is weaker than the additivity property, which plays a role in the axiomatic characterization of the Shapley value: together with individual rationality and efficiency additivity implies the minimal right property. The restricted proportionality property says that for games with minimal right vector zero, the dividend given to the players is proportional to the marginal contribution of the players to the grand coalition.     

On mutation of τ-tilting modules

Mutation of τ-tilting modules is a basic operation to construct a new support τ-tilting module from a given one by replacing a direct summand. The aim of this paper is to give a positive answer to the question posed in [2 Adachi, T., Iyama, O., Reiten, I. (2014). τ-tilting theory. Compos. Math. 150(3):415–452.[Crossref], [Web of Science ®] , [Google Scholar], Question 2.31] about mutation of τ-tilting modules.     

The Structure of Almost Quasi-Regular Rings

Let R be a ring. It is well-known that R is a semigroup with respect to the composition a b=a b-ab for a,b∈R. An element a of R is said to be (right; left) quasi-regular if there exists an element b in R such that (a b=0;