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Xi'anitor, S. (Ed.). (2013). Scientia Magna : An International Journal : Volume 3, No. 4, 2007. Retrieved from http://gutenberg.us/

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