4,630 research outputs found
Smarandache Near-rings
Generally, in any human field, a Smarandache Structure on a set A means a
weak structure W on A such that there exists a proper subset B contained in A
which is embedded with a stronger structure S.
These types of structures occur in our everyday's life, that's why we study
them in this book.
Thus, as a particular case:
A Near-ring is a non-empty set N together with two binary operations '+' and
'.' such that (N, +) is a group (not necessarily abelian), (N, .) is a
semigroup. For all a, b, c belonging to N we have (a + b) . c = a . c + b . c
A Near-field is a non-empty set P together with two binary operations '+' and
'.' such that (P, +) is a group (not-necessarily abelian), {P\{0}, .) is a
group. For all a, b, c belonging to P we have (a + b) . c = a . c + b . c
A Smarandache Near-ring is a near-ring N which has a proper subset P
contained in N, where P is a near-field (with respect to the same binary
operations on N).Comment: 200 pages, 50 tables, 20 figure
Smarandache near-rings
The main concern of this book is the study of Smarandache analogue properties of near-rings and Smarandache near-rings; so it does not promise to cover all concepts or the proofs of all results
Characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals
In this paper, we give characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals (resp. (∈, ∈ ∨q)-fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (∈, ∈ ∨q)-fuzzy ideals and (∈, ∈ ∨q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is (∈, ∈ ∨q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy ideals (resp. (∈, ∈ ∨q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed
Algebraic Structures using Natural Class of Intervals
This book has eleven chapters. Chapter one describes all types of natural
class of intervals and the arithmetic operations on them. Chapter two
introduces the semigroup of natural class of intervals using R or Zn and study
the properties associated with them. Chapter three studies the notion of rings
constructed using the natural class of intervals. Matrix theory using the
special class of intervals is analyzed in chapter four of this book. Chapter
five deals with polynomials using interval coefficients. New types of rings of
natural intervals are introduced and studied in chapter six. The notion of
vector space using natural class of intervals is built in chapter seven. In
chapter eight fuzzy natural class of intervals are introduced and algebraic
structures on them is built and described. Algebraic structures using natural
class of neutrosophic intervals are developed in chapter nine.Chapter ten
suggests some possible applications. The final chapter proposes over 200
problems of which some are at research level and some difficult and others are
simple.Comment: 170 pages; Published by The Educational Publisher Inc in 201
CHARACTERIZATION OF ORDERED SEMIGROUPS BASED 0N (|;qk)-QUASI-COINCIDENT WITH RELATION
Based on generalized quasi-coincident with relation, new types of fuzzy bi-ideals of an ordered semigroup S are introduced. Level subset and characteristic functions are used to linked ordinary bi-ideals and (2;2_(|;qk))fuzzy bi-ideals of an ordered semigroup S: Further, upper/lower parts of (2;2 _(|;qk))-fuzzy bi-ideals of S are determined. Finally, some well known classes of ordered semigroups like regular, left (resp. right) regular and completely regular ordered semigroups are characterized by the properties of (2;2_(|;qk))-fuzzy bi-ideals
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