JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

On Abelian extensions of Hom-δ-Jordan Lie triple systems

MA Li-li, WU Di, LI Qiang, XU Jing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 1-5. doi:10.6040/j.issn.1671-9352.0.2021.684

Abstract ( 668 )

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Cohomology theory of Hom-δ-Jordan Lie triple systems is introduced. The 3-cocycle is obtained by the section of Hom-δ-Jordan Lie triple systems. The structure of a Hom-δ-Jordan Lie triple system is given using representations and 3-cocycles. Sufficient and necessary condition for the equivalence of Abelian extensions of Hom-δ-Jordan Lie triple systems is shown.

On the characterizations of P-principally weakly injective acts

QIAO Hu-sheng, YUAN Ying-min

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 6-10. doi:10.6040/j.issn.1671-9352.0.2021.694

Abstract ( 994 )

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Let S be a monoid and P be a nonempty subset of S. A new kind of principally weakly injective act is defined, which is based on the embedding principal right ideals generated by elements in P and is called P-principally weakly injective act. Using this new property, the characterizations of some new classes of monoids are given.

Properties of amalgamated coproduct AEuclid ExtraCA@^BA

LI Xiao-xia, QIAO Hu-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 11-15. doi:10.6040/j.issn.1671-9352.0.2021.654

Abstract ( 430 )

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Let S be a monoid, A a right S-act and B a proper subact of A. The general amalgamated coproduct AEuclid ExtraCA@^BA is investigated. If taking A be S, B is the proper right ideal of S, then amalgamated coproduct AEuclid ExtraCA@^BA is exactly the important tool A(I)to study the homological classification of monoids. We discuss the equivalent characterizations of the amalgamated coproduct AEuclid ExtraCA@^BA satisfying condition(E'), condition(EP), condition(PF), etc. Finally, the corresponding results of the A(I)is generalized.

Property and structure of rectangular Clifford bi-semirings

WEI Meng-jun, LI Gang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 16-20. doi:10.6040/j.issn.1671-9352.0.2021.802

Abstract ( 423 )

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Feckly McCoy and feckly Armendariz rings

JIANG Mei-mei, WANG Yao, REN Yan-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 21-27. doi:10.6040/j.issn.1671-9352.0.2021.625

Abstract ( 386 )

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To discuss the various extension properties of feckly McCoy rings and feckly Armendariz rings, it is proved that(1)let R be a feckly Armendariz ring with J(R［x］)=J(R)［x］, if for each principal right ideal pR⊈J(R), rJR(pR)=aR where a∈J(R), then for each principal right ideal f(x)R［x］⊈J(R［x］), rJ_R［x］(f(x)R［x］)is generated as an ideal by an element which is in the Jacobson radical of R［x］. (2)let R be a feckly reduced ring with J(R［x］)=J(R)［x］, R is a right J-APP-ring if and only if R［x］ is a right J-APP-ring. These deepen the study of these two new classes of rings.

Gorenstein DG-injective complexes

YIN Jun-qi, YANG Gang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 28-33. doi:10.6040/j.issn.1671-9352.0.2021.727

Abstract ( 473 )

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A notion of Gorenstein DG-injective complexes is introduced and some properties of these complexes are discussed. It is proven that a complex G is Gorenstein DG-injective if and only if G_n is Gorenstein injective in R-Mod for each n∈Z and the complex HomR(E,G) is exact whenever E is a DG-injective complex.

Linear independence of cluster monomials of cluster algebras of type G2 via categorification

GAO Xin-zhao, XIE Yun-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 34-38. doi:10.6040/j.issn.1671-9352.0.2021.697

Abstract ( 447 )

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Using the method of categorization, Fomin-Zelevinskys conjecture about the linear independence of cluster monomials in all cluster algebras holds for cluster algebras of type G₂ is proved, by establishing the Caldero-Chapoton formula from the indecomposable rigid objects in the category of finitely generated modules of the cluster tilted algebra to the cluster variables of the corresponding cluster algebra.

Applications of Frobenius pairs

REN Ye-fei, LIANG Li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 39-43. doi:10.6040/j.issn.1671-9352.0.2021.661

Abstract ( 443 )

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The applications of Frobenius pairs to Gorenstein projective dimensions and Gorenstein flat dimensions is studied. In particular, a classical result by Holm is improved.

n-Gorenstein projective modules over formal triangular matrix rings

NIU Shao-hua, YANG Gang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 44-49. doi:10.6040/j.issn.1671-9352.0.2021.723

Abstract ( 394 )

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Let n be an integer, T=(A 0U B) a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule, _BU is projective, U_A has finite flat dimension. It is proved that, if a left T-module (M1M2)_φ^M is n-Gorenstein projective, then M1 is (n-1)-Gorenstein projective in A-Mod, M₂/Im(φ^M)is n-Gorenstein projective in B-Mod, and φ^M:U⊗_AM1→M2 is a monomorphism. Conversely, if M1 is n-Gorenstein projective in A-Mod, M₂/Im(φ^M) is n-Gorenstein projective in B-Mod, and φ^M:U⊗_AM1→M2 is a monomorphism, then the left T-module (M1M2)_φ^M is n-Gorenstein projective.

A new condition implying the Foxbys conjecture to hold

SUN Jiang-shuai, LIANG Li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 50-51. doi:10.6040/j.issn.1671-9352.0.2021.686

Abstract ( 514 )

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A new sufficient condition implying the Foxbys conjecture to hold on noncommutative rings is given by constructing a push-out graph.

Torsionfreeness and reflexivity under Frobenius extensions

ZHOU Rui, ZHAO Zhi-bing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 52-58. doi:10.6040/j.issn.1671-9352.0.2021.623

Abstract ( 507 )

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Let A/R be a Frobenius extension of rings, we prove that torsionfreeness and reflexivity of modules are preserved under Frobenius extension, that is, for an A-module M, M_A is torsionfree(resp. reflexive)as an A-module if and only if M is torsionfree(resp. reexive)as an R-module.

Ramanujan unitary one-matching bi-Cayley graphs over finite commutative rings

GOU Xiao-li, WANG Wei-zhong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 59-65. doi:10.6040/j.issn.1671-9352.0.2022.004

Abstract ( 522 )

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Let R be a finite commutative ring with unit element 1≠0, and let G_R=BC(R; R^×, R^×, {0})denote the one-matching bi-Cayley graph over R, where R^× is the set of units of R. A k-regular graph G is called a Ramanujan graph if any eigenvalue λ of G with |λ|≠k satisfies |λ|≤2(k-1)1/2. A necessary and sufficient condition for G_R and its line graph to be Ramanujan is given.

On minimum Steiner k-Wiener index of trees with perfect matching

LAI Jin-hua, LIU Meng-meng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 66-71. doi:10.6040/j.issn.1671-9352.0.2020.683

Abstract ( 511 )

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Let G be a connected graph. For 2≤k≤n-1, the Steiner k-Wiener index SW_k(G) is defined as SW_k(G)=∑_{S⊆V(G),|S |=k}d_G(S)where d_G(S) is the Steiner distance of S, the edges of the minimum connected tree of vertex set S in G. A lower bound on Steiner k-Wiener index for trees with perfect matching is given and the extremal graph is characterized.

General p-neighbor integrity of graphs

CUI Chen, WEI Zong-tian

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 72-78. doi:10.6040/j.issn.1671-9352.0.2021.445

Abstract ( 442 )

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In networks, a failed vertex will lead to its neighborhood fail with a certain probability p. Based on this, the concept of general p-neighbor integrity of graphs is proposed, and therefore the concept of integrity and neighbor integrity are unified by the failure probability. Through the parameter calculation of parameter values, the analysis of the relationship with failure probability p and the parameter value comparison of several graphs with the same order, it is shown that this parameter can measure network invulnerability more accurately.

Complete convergence of weighted sums for END sequence under sub-linear expectation space

JIA Cheng-cheng, WU Qun-ying

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 79-87. doi:10.6040/j.issn.1671-9352.0.2021.780

Abstract ( 475 )

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Using the exponential inequality in the sub-linear expectation space as a research tool, under the condition of 1/α+1/β=1/p, C_(-overV)(|X|^rp)<∞, according to this exponential inequality, the complete convergence of the weighted sum of random variable sequences in the traditional probability space is extended to the sublinear expectation space.

A class of maximal inequalities for the functions of demimartingales and N-demimartingales

LU Ya-li, FENG De-cheng, LIN Xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 88-91. doi:10.6040/j.issn.1671-9352.0.2021.455

Abstract ( 460 )

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A class of maximal inequalities for the functions of demartingales and N-demimartingales were given by using upcrossing inequality for demimartingales, downcrossing inequality for N-demimartingales and their maximal inequalities.

Nonlinear maps preserving mixed triple η-products between factors

ZHANG Fang-juan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 92-96. doi:10.6040/j.issn.1671-9352.0.2021.056

Abstract ( 577 )

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Let η∈C\{0,-1}and let φ be a not necessarily linear bijection between two factors, satisfying φ(I)=I and preserving mixed triple η-product. It is showed that φ is a linear *-isomorphism if η is not real and φ is either a linear *-isomorphism or a conjugate linear *-isomorphism if η is real.

A class of non-global nonlinear triple higher derivable maps on generalized matrix algebras

FEI Xiu-hai, ZHANG Hai-fang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 97-105. doi:10.6040/j.issn.1671-9352.0.2021.247

Abstract ( 524 )

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Let G be a 2-torsion free generalized matrix algebra with MN=0=NM,Q={A∈G:A²=0} and D={d_n}_n∈N be a sequence mapping from G into itself(without assumption of additivity). In this paper, it is shown that if D satisfies d_n(ABC)=∑_r+s+t=nd_r(A)d_s(B)d_t(C)for all n∈N,A,B,C∈G with ABC∈Q, then D is an additive higher derivation. As its applications get that the similar conclusion on Triangular algebras.

Characteristic polynomials for the generic arrangements of type D_n

ZHANG Miao, QIANG Jing-jing, GAO Rui-mei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(10): 106-110. doi:10.6040/j.issn.1671-9352.0.2021.611

Abstract ( 297 )

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Assume that W is a Weyl group of type D_n in a Euclidean space with dimension n. A generic arrangement of type D_n is one that consists of hyperplanes whose normal vectors are the positive roots of W. It is denoted by A(D_n). To begin with, a one-to-one connection between the signed graphs with no loops and the sub-arrangements of A(D_n) is established. Then, the sufficient and necessary condition for the linear dependence of signed circles are studied. In the end, from the point of view of signed graphs, the necessary and sufficient conditions for linear independence of sub-arrangements of A(D_n) are given. On this basis, the concrete calculation method of characteristic polynomials of A(D_n) and its sub-arrangements are given.

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