JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

An example of semicommutative Armendariz ring

MA Jing, GUO Ying, SUN Cheng-xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 1-6. doi:10.6040/j.issn.1671-9352.0.2014.242

Abstract ( 1052 )

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An example of semicommutative Armendariz ring is given. We prove that if R is a reduced ring and α,β,γ are compatible endomorphisms of R, then the subring

of the matrix ring M₃(R) is a semicommutative Armendariz ring.

Copure projective dimensions under Hopf extensions

CHEN Xiu-li, CHEN Jian-long

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 7-10. doi:10.6040/j.issn.1671-9352.0.2014.332

Abstract ( 1100 )

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Let H be a finite dimensional Hopf algebra and A be an algebra over a fixed field k. It is proved that the left copure projective dimension of A＃H and that of A is the same when H is semisimple and the extension A/A^H is H^*-Galois. Moreover, it is shown that A＃H is QF if and only if A is QF. Using (co)induction functors, we study the relations between copure projective dimensions in A＃H-Mod and the counterparts in A^H-Mod.

M-Weak quasi McCoy rings

FEI Pan-pan, WU Jun, ZHU Li-min

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 11-16. doi:10.6040/j.issn.1671-9352.0.2014.126

Abstract ( 1188 )

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For a monoid M, this paper introduce M-Weak quasi McCoy rings, study the basic properties of M-Weak quasi McCoy rings, give some equivalent characteristics of M-Weak quasi McCoy rings and discuss the relationships between M-Weak quasi McCoy rings and the other rings.

Anick resolution and some homological properties of quantum group U_q(sl₂)

GAO Zhen-zhen, YANG Shi-lin, OBUL Abdukadir

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 17-27. doi:10.6040/j.issn.1671-9352.0.2014.178

Abstract ( 1065 )

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By using the ö-Shirshov basis and the method of Anick, we construct the Anick resolution for the quantum enveloping algebra U_q(sl₂) As an application, we consider some homological properties and the Poincaré series of U_q(sl₂)

Stability of G_C-projective modules

ZHANG Ya-feng, ZHANG Wen-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 28-32. doi:10.6040/j.issn.1671-9352.0.2014.072

Abstract ( 953 )

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M-type modules are defined, it is proved that if an exact complex of G_C-projective modules

, such that the complexes Hom_R(G,H) and Hom_R(H,G) are exact for every G_C-projective module H, then the modules Ker(d_i) are still G_C-projective modules for every i∈Z.

EP-injectivity and von Neumann regularity of rings

LU Qi, YIN Xiao-bin, BAO Hong-wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 33-37. doi:10.6040/j.issn.1671-9352.0.2014.166

Abstract ( 1192 )

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Some equivalent definitions of EP-injective rings are given. An example is given to show that EP-injective ring needs not be GP-injective. We prove that assume that R is semiperfect and left EP-injective. If Soc(_RR) is essential in _RR, then R is left and right Kasch.

Kegel theorem for generalized Lie algebras

CHEN Hua-xi, ZHANG Cui-bin, DONG Li-hong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 38-44. doi:10.6040/j.issn.1671-9352.0.2014.265

Abstract ( 1131 )

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Let π be a group and H,σa cotriangular Hopf πcoalgebra. The difinitions of a class of generalized Lie algebras in the category of right π-comodules over H are introduced, and an analogue of the classical Kegel's theorem is obtained.

Quadratic residue codes over F_l+vF_l+v²F_l

LIU Cai-ran, SONG Xian-mei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 45-49. doi:10.6040/j.issn.1671-9352.0.2014.260

Abstract ( 1174 )

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Quadratic residue codes over the ring R=F_l+vF_l+v²F_l are defined in terms of their idempotent generators, where v³=v and l is an odd prime. The relations among the four codes are discussed. Furthermore, the relations between the four codes and their dual codes are obtained.

Some properties of primitive ideal submodules in Hilbert C^*-modules

YANG Gong-lin, JI Pei-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 50-55. doi:10.6040/j.issn.1671-9352.0.2014.158

Abstract ( 815 )

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The definition of the primitive ideal submodules in Hilbert C^*-modules is given. Some properties of primitive ideal submodule space and the spectrum space in Hilbert C^*-modules are studied. It is shown that these results extend and improve the existing results.

A note on operator matrixs

CUI Miao-miao, WANG Bi-yu, CAO Xiao-hong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 56-61. doi:10.6040/j.issn.1671-9352.0.2014.075

Abstract ( 1136 )

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Let H be a separable complex Hilbert space and B(H) be the algebra of all bounded linear operators. Let

be an operator matrix, which acts on B(H⊕H). We character the compact perturbations of single-valued extension property and Browder theorem about T by A's respectively, when B^k=0(k∈N and k≥2), AB=BA.

Reliability analysis of a warm standby repairable system with unreliable transfer switch

ZHANG Quan, HAN Yang, GUAN Bao-ling, LI Yan-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 62-65. doi:10.6040/j.issn.1671-9352.0.2014.087

Abstract ( 1097 )

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A warm standby repairable system consisting of two different units and one repairmanis was studied.The switch is not completely reliable, as long as the switch failure, system failure immediately. It is assumed that the working time distributions and the repair time distributions of the two units and the transfer switch are both exponential, and unit 1 is given priority than unit 2 in use and repair. Both unit 1 and unit 2 are repaired “as good as new”. The switch taking change of the switching work between the working unit and the standby unit is an important part of the system and has the priority in repair. Under these assumptions, the Markov process governing the system is constructed and some important reliability indexes are derived by using the aggregated stochastic processes and the Laplace transform. Finally, a numerical example is given to illustrate the theoretical results of the model.

Superconvergence analysis and extrapolation of bilinear finite element for Schrödinger equation

WANG Ping-li, SHI Dong-yang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 66-71. doi:10.6040/j.issn.1671-9352.0.2014.128

Abstract ( 1301 )

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The bilinear finite element approximation is mainly discussed for Schrödinger equation. The superclose property with O(h²)order is obtained in H¹-norm by use of the derivative transfering skill and the high accuracy results of the element. Also, the global superconvergence result is given in H¹-norm through the interpolation post-processing technique. Furthermore, through constructing a new extrapolation scheme, the extrapolation solution with O(h³)order is deduced which is two order higher than the traditional error estimate.

Characterization of bicompletable interval-valued fuzzy quasi-metric spaces

LU Han-chuan, LI Sheng-gang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 72-77. doi:10.6040/j.issn.1671-9352.0.2013.548

Abstract ( 1182 )

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We generalize the notions of interval-valued fuzzy metric in the quasi-metric background. The main results of this paper are: (1) the isometric extension theorem of interval-valued fuzzy quasi-metric space is given; (2) it is proved that every interval-valued fuzzy quasi-metric space has bicompletion and is unique up to isometry; (3) a method to construct the interval-valued fuzzy quasi-metric space bicompletion is given, and a equivalent characterization of interval-value fuzzy quasi-metric spaces is obtained which can be bicompletable.

The characterizations of lattice-valued fuzzy lower approximation operators by a unique axiom

LI Ling-qiang, LI Qing-guo

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 78-82. doi:10.6040/j.issn.1671-9352.0.2014.105

Abstract ( 1368 )

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Axiomatic approaches are important in the study of rough set theory. Generally, the axiomatic systems of rough sets consist of more than one axiom. In this paper, under the residuated lattice-valued context, we use only one axiom to describe the lower approximation generated by the lattice-valued fuzzy relations and a series of special lattice-valued fuzzy relations.

Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras

LIU Chun-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 83-89. doi:10.6040/j.issn.1671-9352.0.2013.648

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The theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras is studied systematically. Firstly, two notions of interval valued (∈,∈∨ q)-fuzzy involution filters and interval valued (∈,∈∨ q)-fuzzy associative filters are introduced and some characterizations of them are obtained. Secondly, the relations among all kinds of interval valued (∈,∈∨ q)-fuzzy filters are discussed. It is proved that an interval valued fuzzy set is an interval valued (∈,∈∨ q)-fuzzy Boolean (implicative) filter if and only if it is both an interval valued (∈,∈∨ q)-fuzzy positive implicative and an interval valued (∈,∈∨ q)-fuzzy involution filter.

Random function inverse P-sets and its characteristics depending on attributes

ZHANG Yue-yun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(10): 90-94. doi:10.6040/j.issn.1671-9352.0.2014.141

Abstract ( 1343 )

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By introducing random characteristics into function inverse P-sets and improving it, the concept and structure of random function inverse P-sets (packet sets) is proposed, which is an ordered pair of cantor sets composed of random function internal inverse P-set and random function outer inverse P-set. Also, it is pointed that random function inverse P-sets is an expansion model of function inverse P-sets, while function inverse P-sets is a case of random function inverse P-sets. Based on the concepts of random function inverse P-sets, its random feature theorems and the dependent relationship theorems between random function inverse P-sets and its attributes are obtained. So the random function inverse P-sets extend the application field of function inverse P-sets.

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