JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Pure projective dimensions on recollements of Abelian categories

YAN Mei-qi, YAO Hai-lou

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 1-5. doi:10.6040/j.issn.1671-9352.0.2021.332

Abstract ( 1018 )

PDF (394KB) ( 373 )

Save

References | Related Articles | Metrics

The concepts of pure projective dimensions in Abelian categories are introduced. Let R_ab(A,B,C )be a recollement of Abelian categories where A,B and C are Abelian categories, the relations of pure projective objects and pure projective dimensions of objects in three Abelian categories are studied. As applications, the pure projective modules and pure projective dimensions over formal triangular matrix rings are studied. Finally, it is proved that pure projective dimension of B is finite if and only if the pure projective dimensions of A and C are finite under some conditions.

Rota-Baxter paired module system and curved Rota-Baxter paired module system

ZHANG Yu-xin, ZHENG Si-hang, FANG Ying, ZHENG Hui-hui, ZHANG Liang-yun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 6-14. doi:10.6040/j.issn.1671-9352.0.2020.619

Abstract ( 924 )

PDF (393KB) ( 338 )

Save

References | Related Articles | Metrics

Firstly, the concepts of Rota-Baxter paired module system and curved Rota-Baxter paired module system are introduced. Then, pre-Lie module and dendriform module are constructed from them. Lastly, Rota-Baxter paired module system and curved Rota-Baxter paired module system are constructed from the integral in semisimple Hopf algebra.

*-Armendariz rings

LI Xin, WANG Yao, REN Yan-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 15-24. doi:10.6040/j.issn.1671-9352.0.2021.049

Abstract ( 889 )

PDF (432KB) ( 552 )

Save

References | Related Articles | Metrics

The properties of Armendariz rings with an involution are investigated, some examples of this class rings are given, and their extensions and the relationship between*-Armendariz rings and related rings are studied.

A note on DG-Ding injective complexes

LIU Yi-fu, LU Bo

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 25-31. doi:10.6040/j.issn.1671-9352.0.2020.685

Abstract ( 777 )

PDF (381KB) ( 611 )

Save

References | Related Articles | Metrics

Let G be a complex. DG-Ding injective complex is defined and studied. It is proved that G is a DG-Ding injective complex if and only if G is exact with that each Z_n(G)is a Ding injective module for any integer n and any homomorphism f:J→G is null homotopic for any DG-FP-injective complex J when R is a left coherent ring.

Some properties of JQ rings

MA Guang-lin, WANG Yao, REN Yan-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 32-38. doi:10.6040/j.issn.1671-9352.0.2021.043

Abstract ( 651 )

PDF (364KB) ( 280 )

Save

References | Related Articles | Metrics

The concept of JQ rings is introduced. A ring R is called a JQ ring if its Jacobson radical coincides with the set of all quasi regular elements. We give some examples of JQ rings, and discuss the extension properties of JQ rings.

The left-star order for idempotent operators

HAO Hong-yan, LI Yuan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 39-44. doi:10.6040/j.issn.1671-9352.0.2020.421

Abstract ( 641 )

PDF (336KB) ( 204 )

Save

References | Related Articles | Metrics

It is investigated that the characterizations of all idempotent operators on Hilbert space H with respect to the left-star order, which is defined by A^*A=A^*B and R(A)⊆R(B). Let A and B be two idempotent operators, the equivalent condition of A*≤B and the representation of operator matrix form is given. Meanwhile, the existence and representation of A∨B(supremum)and A∧B(infimum)of the star order when A*≤B is discussed.

The property and structure of left Clifford bi-semirings

WEI Meng-jun, LI Gang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 45-48. doi:10.6040/j.issn.1671-9352.0.2021.157

Abstract ( 817 )

PDF (306KB) ( 287 )

Save

References | Related Articles | Metrics

The distributive lattice of bi-semirings and band bi-semirings are defined. Using these two definitions and the properties of the left Clifford semigroup, the definitions of the left bi-ring and the left Clifford bi-semiring are given. The necessary and sufficient conditions for a bi-semiring to be a left bi-ring and a bi-semiring to be a left Clifford bi-semiring are obtained.

On the cyclic S-acts satisfying condition(P')

LEI Yan, QIAO Hu-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 49-52. doi:10.6040/j.issn.1671-9352.0.2020.651

Abstract ( 3627 )

PDF (307KB) ( 238 )

Save

References | Related Articles | Metrics

Let S be a monoid and ρ be a right congruence on S, S/ρ be a cyclic right S-act. The homological classification problem of cyclic right S-acts satisfying condition(P')with respect to condition(P), condition(PF″), weakly pullback flat, strong flat and projective properties are discussed.

On Coleman outer automorphism groups of a class of metacyclic groups

Yihuo A-ga, HAI Jin-ke

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 53-57. doi:10.6040/j.issn.1671-9352.0.2020.680

Abstract ( 963 )

PDF (309KB) ( 291 )

Save

References | Related Articles | Metrics

It is proved that the Coleman outer automorphism group of a class of metacyclic groups is either 1 or an elementary Abelian 2-group by using the projection limit property of the group.

A note on a finite group in which all non-nilpotent maximal subgroups are normal has a Sylow tower

SHI Jiang-tao, REN Hui-xuan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 58-60. doi:10.6040/j.issn.1671-9352.0.2020.623

Abstract ( 966 )

PDF (291KB) ( 481 )

Save

References | Related Articles | Metrics

Let G be a finite group in which all non-nilpotent maximal subgroups are normal. Without applying the solvability of G, we prove that G has a Sylow tower.

Homogeneous Rota-Baxter operators of 3-Lie algebra T

BAI Rui-pu, LIU Pei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 61-66. doi:10.6040/j.issn.1671-9352.0.2021.097

Abstract ( 791 )

PDF (355KB) ( 578 )

Save

References | Related Articles | Metrics

Structure of homogeneous Rota-Baxter operators θ on the classical Nambu 3-Lie algebra T=∑_{l∈z_≥1} Fy sin(lx)∑_{r∈z_≥}0Fz cos(rx)over the real field F of weight 1 and weight 0 is studied, where θ satisfies that there are two additive mappings α, β from the integers to F such that θ(y sin(lx))=α(l)y sin(lx), θ(z cos(rx))=β(r)z cos(rx). It is proved that there exist 10 non-zero homogeneous Rota-Baxter operators of weight 1, and 4 non-zero homogeneous Rota-Baxter operators of weight 0, and concrete expression of them are given.

Enumerations of equivalent classes with actions of permutation group on a class of mapping set

TANG Shan-gang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 67-75. doi:10.6040/j.issn.1671-9352.0.2020.153

Abstract ( 887 )

PDF (422KB) ( 493 )

Save

References | Related Articles | Metrics

Enumerations of equivalent classes with action of permutation group on a class of mapping set are studied by using Burnside-Polya enumerating theorem, principle of inclusion-exclusion and other combinatorial analysis. Enumerations of equivalent classes and its plane circular alternating permutation enumerations, space circular alternating permutation enumerations and combinatorial identities with actions of cycle group and dihedral group on a class of mapping set are obtained. These results generalize some known results.

Constitutions and Abelian extensions of δ-Jordan Lie supertriple systems

MA Li-li, DAI Di, LI Qiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 76-80. doi:10.6040/j.issn.1671-9352.0.2021.009

Abstract ( 752 )

PDF (326KB) ( 250 )

Save

References | Related Articles | Metrics

The 3-cocycle is given using the Abelian extension of δ-Jordan Lie supertriple systems. The δ-Jordan Lie supertriple system is constructed by the representation and a 3-cocycle. It is shown that two Abelian extensions of δ-Jordan Lie supertriple systems are equivalent if and only if 3-cocycles are in the same cohomology class.

Strongly Gorenstein projective objects in comma categories

CHEN Mei-hui, LIANG Li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 81-85. doi:10.6040/j.issn.1671-9352.0.2020.709

Abstract ( 791 )

PDF (408KB) ( 538 )

Save

References | Related Articles | Metrics

Introduce the comma category(F,B )and give an equivalent characterization of strongly Gorenstein projective objects in(F,B )in terms of strongly Gorenstein projective objects in A and B.

A characterization of Gorenstein FP-injective modules over triangular matrix rings

WU De-jun, ZHOU Hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 86-93. doi:10.6040/j.issn.1671-9352.0.2021.062

Abstract ( 844 )

PDF (369KB) ( 417 )

Save

References | Related Articles | Metrics

Let T=(A 0U B) be a formal triangular matrix ring. A characterization of Gorenstein FP-injective left T-modules is given.

Some notes on periodic modules

WANG Jian, WU Jin-yong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 94-98. doi:10.6040/j.issn.1671-9352.0.2021.139

Abstract ( 650 )

PDF (342KB) ( 215 )

Save

References | Related Articles | Metrics

Let R be a ring and A a class of left R-modules. Assume that A is a projectively resolving precovering class, using dimension shifting, a sufficient condition for an A -periodic left R-module M in A is obtained by applying the properties of A -dimensions and self-orthogonal modules. As an application, some characterizations of finiteness of the left global dimension of R are given which provided that the left Gorenstein global dimension of R is finite. In addition, under an extra condition, a characterization of infinitely presented partial tilting modules in A^⊥ is supplied.

Gorenstein weak flat modules and dimension over right GWF-closed rings

SONG Yan-hui, GUO Ting

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 99-104. doi:10.6040/j.issn.1671-9352.0.2021.066

Abstract ( 728 )

PDF (518KB) ( 350 )

Save

References | Related Articles | Metrics

The properties of Gorenstein weak flat modules and Gorenstein weak flat dimension over right GWF-closed rings are investigated in this paper, and the Gorenstein weak flat dimension of modules is characterized.

PGF-modules and strongly semi-Gorenstein-projective modules

BAI Jiu-hong, LIANG Li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(8): 105-110. doi:10.6040/j.issn.1671-9352.0.2021.160

Abstract ( 720 )

PDF (337KB) ( 338 )

Save

References | Related Articles | Metrics

Let SSGP denote the class of all strongly semi-Gorenstein-projective modules. Some relations between PGF-modules and strongly semi-Gorenstein-projective modules are given, and over an arbitrary ring R, SSGP∩PGF^~=PGF is proved. It is got that SSGP=PGF if and only if SSGP⊆PGF^~, where PGF is the class of all PGF-modules, and PGF^~ is the class of all R-modules with finite PGF-dimension. Finally, the finitistic PGF-dimension of a ring R is equal to the finitistic projective dimension is proved.

Table of Content