In this paper we study the notion of Smarandache semirings and semifields and obtain some interesting results about them. We show that not every semiring is a Smarandache semiring. We similarly prove that not every semifield is a Smarandache semifield. We give several examples to make the concept lucid. Further, we propose an open problem about the existence of Smarandache semiring S of finite ...

In this article we present two new results concerning the Smarandache Ceil function. The first result proposes an equation for the number of fixed-point number of the Smarandache ceil function. Based on this result we prove that the average of the Smarandache ceil function is ) (n Θ .

In his recent paper[l], Sastry defines two triangles T(a,b,c) and T(a',b',c') to be Smarandache related ifS(a) = Sea'), S(b) = S(b') and S(c) = S(c'). The function S is known as the Smarandache function and is defmed in the following way. For n any integer greater than zero, the value of the Smarandache function Sen) is the smallest integer m such that n divides m!. He closes the paper by askin...

In this paper three problems posed in [1J and concerning the Smarandache LeM sequence have been analysed. Introduction In [1] the Smarandache LCM . sequence is defined as the least common mUltiple (LCM) of (1,2,3, .,. ,n) : 1,2,6, 12,60,60,420,840,2520,2520,27720,27720,360360, 360360, 360360, 720720 ...... . In the same paper the following three problems are reported: 1. If a(n) is the n-th ter...

In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper BCC-algebras, and then we determine the relationships between these hyper ideals. © 2011 Elsevier Ltd. All rights reserved.

A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a n-manifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equi...

1 Department of Mathematics, Faculty of Sciences, University of Cankiri Karatekin, Cankiri 18100, Turkey 2 School of Mathematics & Statistical Sciences, Arizona State University, Room PSA442, Tempe, AZ 85287-1804, USA 3Department of Mathematics, Faculty of Sciences and Art, University of Kırıkkale, Kırıkkale 71450, Turkey 4University of Kragujevac, Faculty of Science, Department of Mathematics ...

1 Department of Mathematics, Faculty of Sciences, University of Çankiri Karatekin, 18100 Çankiri, Turkey 2 School of Mathematics & Statistical Sciences, Room PSA442, Arizona State University, Tempe, AZ 85287-1804, USA 3Department of Mathematics, Faculty of Sciences and Arts, University of Kirikkale, 71450 Kirikkale, Turkey 4Department of Mathematics and Informatics, Faculty of Science, Universi...

The study of primality for the Smarandache sequences represents a recent research direction on the Smarandache type notions. A few articles that were published recently deal with the primality of the direct and reverse Smarandache sequences. The primality of Smarandache symmetric sequences has not been studied yet. This article proposes some results concerning the non-primality of these symmetr...