JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

On silting comodules

YUAN Qian-qian, YAO Hai-lou

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 1-7. doi:10.6040/j.issn.1671-9352.0.2021.503

Abstract ( 848 )

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The concept of silting comodules in comodule category is introduced, and their properties are discussed. Based on the canonical methods of representation theory of algebra, we study silting comodules and partial silting comodules, and obtain the Bongartz theorem for the complement of partial silting comodules.

Equivalent characterizations of strong right mininjective, semiperfect, right PF and clean triangular matrix rings of order n

TANG Guo-liang, CHEN Ling-qiao, DI Zhen-xing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 8-13. doi:10.6040/j.issn.1671-9352.0.2021.055

Abstract ( 934 )

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Let n be a given positive integer. The equivalent characterizations of strong right mininjective, semiperfect, right PF and clean triangular matrix rings of order n are given.

2-nil-clean rings

CHEN Jiang-huan, WANG Yao, REN Yan-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 14-22. doi:10.6040/j.issn.1671-9352.0.2021.324

Abstract ( 893 )

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The concept of 2-nil-clean rings is introduced. A ring R is called 2-nil-clean if every element in R is the sum of an idempotent and two nilpotents. Making use of the classical methods in ring theory, it is investigated that some properties of them and the relationship between 2-nil-clean rings and related rings.

Relative derived category with respect to a duality pair

LIU Yan-ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 23-30. doi:10.6040/j.issn.1671-9352.0.2021.506

Abstract ( 704 )

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The relative derived categories with respect to Gorenstein(L,A)-projective and Gorenstein(L,A)-injective modules are introduced, where(L,A)is a fixed complete duality pair. A triangle-equivalence and description of morphisms in such relative derived categories are given. We also discuss a generalized Tate cohomology and obtain Avramov-Martsinkovsky exact sequences.

n-Gorenstein graded projective(injective)modules

YUAN Qian, ZHANG Wen-hui, ZHANG Ming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 31-37. doi:10.6040/j.issn.1671-9352.0.2021.061

Abstract ( 518 )

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Let G be a multiplicative group, R be a G-graded ring, n-Gorenstein graded projective and n-Gorenstein graded injective modules are introduced, the homological properties and the dimensions of the two types of modules are investigated. It is proved that if the graded R-module M satisfies n-G-gr-pdRM=m<∞, then exists an exact sequence 0→K→G→M→ 0, where G is n-Gorenstein graded projective R-module and pdRK=m-1.

Gorenstein FP-injective modules over formal triangular matrix rings

YANG Yin-yin, ZHANG Cui-ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 38-44. doi:10.6040/j.issn.1671-9352.0.2021.328

Abstract ( 1008 )

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Let T=(A 0U B) be a formal triangular matrix ring, where A and B are rings and U is (B,A)-bimodule. It is proved that if T is a left cocherent ring, _BU is finitely presented and pd(_BU)<∞, M=(M1M2)_φ^M is Gorenstein FP-injective left T-module, then Ker φ^M^~ is Gorenstein FP-injective left A-module, M2 is Gorenstein FP-injective left B-module, and φ^M^~ is an epimorphism; if T is still a left GFPI-closed ring, then the opposite case holds.

Number of homomorphisms between intra-commutative p-groups and quaternion groups

LIAO Qing-qing, GUO Ji-dong, ZHANG Liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 45-49. doi:10.6040/j.issn.1671-9352.0.2021.411

Abstract ( 938 )

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Based on the group structure and element properties of intra-commutative p-groups and quaternion groups, the number of homomorphisms from a class of intra-commutative p-groups into quaternion groups is calculated. As an application, the conjecture of T.Asai and T.Yoshida is proved to be valid for such groups.

Tropical matrix semigroups

WANG Jing, GONG Chun-mei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 50-55. doi:10.6040/j.issn.1671-9352.0.2021.412

Abstract ( 735 )

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The(*)-Greens relations and regularity of tropical matrix multiplicative semigroups are studied. The equivalent characterizations of the R^* and D ^* relations on tropical matrix multiplicative semigroups are given, the regularity properties of the upper triangular tropical matrix multiplicative semigroups are discussed.

Some studies on condition(E'P)

QIAO Xing-bin, QIAO Hu-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 56-60. doi:10.6040/j.issn.1671-9352.0.2021.345

Abstract ( 1111 )

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Let S be a pomonoid. Condition(E'P)in the category of S-posets is introduced, the equivalent characterizations of cyclic S-posets S/ρ and diagonal S-posets D(S) satisfying condition(E'P)are given, the problem of right S-posets satisfying condition(E'P)which closed under directed colimits is discussed. In addition, the necessary and sufficient condition for cyclic S-posets S/ρ to have condition(E'P)-cover is given.

(~)-Good congruences on Rees matrix semigroups over semiadequate semigroups

CUI Qian, GONG Chun-mei, WANG Hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 61-66. doi:10.6040/j.issn.1671-9352.0.2021.408

Abstract ( 769 )

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The(~)-good congruences of Rees matrix semigroups over semiadequate semigroups with congruence condition are studied. Firstly, some properties of Rees matrix semigroups are given, and then, the(~)-good congruence of such semigroups are characterized by means of(~)-good congruence pairs.

Influence of σ-embedding system of subgroups on the structure of finite groups

MA Xiao-jian, MAO Yue-mei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 67-71. doi:10.6040/j.issn.1671-9352.0.2021.505

Abstract ( 1065 )

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Let ∑={G0≤G1≤…≤G_n-1≤G_n} be a subgroup series of G. A subgroup H of G is said to be ∑-σ-embedded in G if H either covers or avoids every σ-abnormal pair (K,L)such that G_i-1≤Ki for some i. The influence of ∑-σ-embedded subgroups on the structure of finite groups G is studied. Some new conclusions of σ-supersoluble and σ-soluble will be given by using some related theories of σ-solvable groups, properties of complete Hall σ-set and some basic methods of finite group theory.

Estimate involving sum of coefficients of the Rankin-Selberg L-function

LIU Can

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 72-77. doi:10.6040/j.issn.1671-9352.0.2021.603

Abstract ( 806 )

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Let k be an even integer and f(z) be a primitive holomorphic cusp form of weight k for the full modular group Γ=SL₂(Z). Let λ_{sym²f ×sym³f}(n)be the n-th coefficient of Dirichlet series of the Rankin-Selberg L-function L(s,sym²f ×sym³f). Using the breakthroughs of Newton-Thorne on the automorphy of L(s,symjf)on j to study the mean distribution of λ²_{sym²f ×sym³f}(n), a more accurate asymptotic formula can be obtained.

Neighbor sum distinguishing edge coloring of unicyclic graphs

TAN Jun-ming, QIANG Hui-ying, WANG Hong-shen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 78-83. doi:10.6040/j.issn.1671-9352.0.2021.649

Abstract ( 829 )

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A proper k-edge coloring of graph G is a k-neighbor sum distinguishing edge coloring if the sum of all elements in the colors sets of any two adjacent vertices is different. The smallest value k is called the neighbor sum distinguishing edge chromatic number of G. The neighbor sum distinguishing edge chromatic numbers of unicyclic graphs are studied by the methods of analysis and mathematical induction.

Extremal graphs on distance spectral radius of polyomino chains

WU Yi-fan, WANG Guang-fu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 84-91. doi:10.6040/j.issn.1671-9352.0.2021.449

Abstract ( 778 )

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The distance spectral radius of a connected graph G is the largest eigenvalue of its distance matrix. The extremal graphs with maximum and minimum distance spectral radius in polyomino chains are determined. Among polyomino chains with n squares, the extremal graph with maximum distance spectral radius is the linear polyomino chain L_n, and the extremal graph with minimum distance spectral radius is the zig-zag polyomino chain Z_n.

Ideal hereditary irresolvable spaces

LU Shi-zhan, LIU Yuan-yuan, CHENG Long-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 92-97. doi:10.6040/j.issn.1671-9352.0.2021.099

Abstract ( 716 )

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Some space properties of the ideal hereditary irresolvable space are researched. It is proved that an ideal hereditary irresolvable space and an ideal scattered space are equivalent, if they are ideal Alexandroff topological spaces.

Stability and extended well-posedness of the solution sets for set optimization problems

MENG Xu-dong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(2): 98-110. doi:10.6040/j.issn.1671-9352.0.2020.343

Abstract ( 748 )

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The stability and extended well-posedness of the approximate solution sets for set optimization problems are studied. The Painlevé-Kuratowski upper convergence and lower convergence of the approximate solution sets for set optimization problems are discussed by assuming the continuity and generalized cone quasi-convexity of objective function. The extended well-posedness and weak extended well-posedness for set optimization problems are analyzed under some appropriate assumptions.

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