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Scientia Magna : An International Journal : Volume 3, No. 4, 2007

By Xi'an, Shaanxi


Description
Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

Excerpt
A structure theorem of right C-rpp semigroups1 Abstract A new method of construction for right C-rpp semigroups is given by using a right cross product of a right regular band and a strong semilattice of left cancellative monoids. Keywords Right C-rpp semigroups, right cross products, right regular bands, left cancellative monoids. x1. Introduction Recall that a semigroup S is called an rpp semigroup if all its principal right ideals aS1, regarded as right S1-systems, are projective. According to J.B. Fountain[5], a semigroup S is rpp if and only if, for any a 2 S, the set Ma=fe 2 E j S1a µ Se and for all x; y 2 S1, ax = ay ) ex = eyg is a non-empty set, where E is the set of all idempotents of S. An rpp semigroup S is called strongly rpp if for every a 2 S, there exists a unique idempotent e in Ma such that ea=a. It is easy to see that regular semigroups are rpp semigroups and completely regular semigroups are strongly rpp semigroups. Thus, rpp semigroups are generalizations of regular semigroups. A strongly rpp semigroups S is said to be a right C-rpp semigroup if L. _ R is a congruence on S and Se µ eS for all e 2 E(S). It is clear that a right C-rpp semigroup is a generalization of a right inverse semigroup (see [8]). Right C-rpp semigroups have been investigated by Guo and Shum-Ren in [3] and [2]. In this paper, we will give another construction of such semigroups by using right cross product of semigroups.

Table of Contents
X. Pan and B. Liu : On the irrational root sieve sequence 1 H. Liu : Sub-self-conformal sets 4 K. Liu : On mean values of an arithmetic function 12 L. Wang and Y. Liu : On an infinite series related to Hexagon-numbers 16 X. Ren, etc. : A structure theorem of right C-rpp semigroups 21 A. R. Gilani and B. N. Waphare : Fuzzy extension in BCI-algebras 26 A. S. Shabani : The Pell's equation x2 ¡ Dy2 = §a 33 L. Cheng : On the mean value of the Smarandache LCM function 41 W. Guan : Four problems related to the Pseudo-Smarandache-Squarefree function 45 Y. Lou : On the pseudo Smarandache function 48 J. L. Gonzalez : A miscellaneous remark on problems involving Mersenne primes 51 Y. Liu and J. Li : On the F.Smarandache LCM function and its mean value 52 N. T. Quang and P. D. Tuan : A generalized abc-theorem for functions of several variables 56 W. Liu, etc. : An assessment method for weight of experts at interval judgment 61 Y. Xue : On the F.Smarandache LCM function SL(n) 69 Y. Zheng : On the Pseudo Smarandache function and its two conjectures 74 Z. Ding : Diophantine equations and their positive integer solutions 77 S. Gou and J. Li : On the Pseudo-Smarandache function 81 B. Liu and X. Pan : On a problem related to function S(n) 84 S. Hussain and B. Ahmad : On closed spaces 87 X. Mu, etc. : A successive linear programming algorithm for SDP relaxation of binary quadratic programming 94 J. L. Gonz¶alez : A note on primes of the form a2 + 1 104 D. Wang : The natural partial order on U-semiabundant semigroups 105 J. Wang : On the value distribution properties of the Smarandache double-factorial function 111 A. Jing and F. Liang : On the factorial base and related counting function 115

 

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