Biring

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Bilagebraic Structures And Smarandache Bialgebraic Structures

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2003-01-01

Bilagebraic Structures And Smarandache Bialgebraic Structures written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.

Generally the study of algebraic structures deals with the concepts like groups, semigroups, groupoids, loops, rings, near-rings, semirings, and vector spaces. The study of bialgebraic structures deals with the study of bistructures like bigroups, biloops, bigroupoids, bisemigroups, birings, binear-rings, bisemirings and bivector spaces. A complete study of these bialgebraic structures and their Smarandache analogues is carried out in this book. For examples: A set (S, +, *) with two binary operations ?+? and '*' is called a bisemigroup of type II if there exists two proper subsets S1 and S2 of S such that S = S1 U S2 and(S1, +) is a semigroup.(S2, *) is a semigroup. Let (S, +, *) be a bisemigroup. We call (S, +, *) a Smarandache bisemigroup (S-bisemigroup) if S has a proper subset P such that (P, +, *) is a bigroup under the operations of S. Let (L, +, *) be a non empty set with two binary operations. L is said to be a biloop if L has two nonempty finite proper subsets L1 and L2 of L such that L = L1 U L2 and(L1, +) is a loop, (L2, *) is a loop or a group. Let (L, +, *) be a biloop we call L a Smarandache biloop (S-biloop) if L has a proper subset P which is a bigroup. Let (G, +, *) be a non-empty set. We call G a bigroupoid if G = G1 U G2 and satisfies the following:(G1 , +) is a groupoid (i.e. the operation + is non-associative), (G2, *) is a semigroup. Let (G, +, *) be a non-empty set with G = G1 U G2, we call G a Smarandache bigroupoid (S-bigroupoid) if G1 and G2 are distinct proper subsets of G such that G = G1 U G2 (neither G1 nor G2 are included in each other), (G1, +) is a S-groupoid.(G2, *) is a S-semigroup.A nonempty set (R, +, *) with two binary operations ?+? and '*' is said to be a biring if R = R1 U R2 where R1 and R2 are proper subsets of R and (R1, +, *) is a ring, (R2, +, ?) is a ring.A Smarandache biring (S-biring) (R, +, *) is a non-empty set with two binary operations ?+? and '*' such that R = R1 U R2 where R1 and R2 are proper subsets of R and(R1, +, *) is a S-ring, (R2, +, *) is a S-ring.

Smarandache Fuzzy Algebra

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2003

Smarandache Fuzzy Algebra written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white.In any human field, a Smarandache n-structure on a set S means a weak structure {w(0)} on S such that there exists a chain of proper subsets P(n-1) in P(n-2) in?in P(2) in P(1) in S whose corresponding structures verify the chain {w(n-1)} includes {w(n-2)} includes? includes {w(2)} includes {w(1)} includes {w(0)}, where 'includes' signifies 'strictly stronger' (i.e., structure satisfying more axioms).This book is referring to a Smarandache 2-algebraic structure (two levels only of structures in algebra) on a set S, i.e. a weak structure {w(0)} on S such that there exists a proper subset P of S, which is embedded with a stronger structure {w(1)}. Properties of Smarandache fuzzy semigroups, groupoids, loops, bigroupoids, biloops, non-associative rings, birings, vector spaces, semirings, semivector spaces, non-associative semirings, bisemirings, near-rings, non-associative near-ring, and binear-rings are presented in the second part of this book together with examples, solved and unsolved problems, and theorems. Also, applications of Smarandache groupoids, near-rings, and semirings in automaton theory, in error correcting codes, and in the construction of S-sub-biautomaton can be found in the last chapter.

The Celebes And Surrounding Islands

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Author : United States. Army. Forces, Far East
language : en
Publisher:
Release Date : 1943

The Celebes And Surrounding Islands written by United States. Army. Forces, Far East and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1943 with Islands of the Pacific categories.

Cases Determined By The St Louis Kansas City And Springfield Courts Of Appeals Of The State Of Missouri

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Author : Missouri. Courts of Appeals
language : en
Publisher:
Release Date : 1931

Cases Determined By The St Louis Kansas City And Springfield Courts Of Appeals Of The State Of Missouri written by Missouri. Courts of Appeals and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1931 with Law reports, digests, etc categories.

Directory Of Geographic Place Names In The Southwest Pacific Area Exclusive Of Continental Australia The Celebes And Surrounding Islands

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Author : United States. Army. Forces, Far East
language : en
Publisher:
Release Date : 1943

Directory Of Geographic Place Names In The Southwest Pacific Area Exclusive Of Continental Australia The Celebes And Surrounding Islands written by United States. Army. Forces, Far East and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1943 with Hainan (China) categories.

Negligence And Compensation Cases Annotated

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Author :
language : en
Publisher:
Release Date : 1962

Negligence And Compensation Cases Annotated written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Employers' liability categories.

Current appellate decisions with supporting pleadings and approved instructions relating to the law of negligence generally, with accompanying editorial comment, cross-references to additional sources, and relevant case annotations.

The Guritan Of Radin Suane

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Author : William Augustus Collins
language : en
Publisher: Brill
Release Date : 1998

The Guritan Of Radin Suane written by William Augustus Collins and has been published by Brill this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Fiction categories.

This study presents the text and translation of an oral epic, or guritan, relating the exploits of Radin Suane, which was recorded during anthropological fieldwork among the Besemah, in the remote highlands of South Sumatra. Documentation of an epic in Besemah, a little known Sumatran-Malay language, will be useful for comparative purposes to specialists in Malaysian and Indonesian languages and literatures. This work is also intended to serve students of ethnography, folklore and oral poetry, as well as general readers who may not be familiar with Sumatran culture. Accordingly, an extensive commentary has been provided to give a cultural context for understanding this epic.

Boot And Shoe Recorder

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Author :
language : en
Publisher:
Release Date : 1954

Boot And Shoe Recorder written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Boot and shoes categories.

Indian Notes And Queries

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Author :
language : en
Publisher:
Release Date : 1886

Indian Notes And Queries written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1886 with Folklore categories.

Directory Of Geographic Place Names In The Southwest Pacific Area Exclusive Of Continental Australia British Solomon Islands

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Author : United States. Army. Forces, Far East
language : en
Publisher:
Release Date : 1943

Directory Of Geographic Place Names In The Southwest Pacific Area Exclusive Of Continental Australia British Solomon Islands written by United States. Army. Forces, Far East and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1943 with Hainan (China) categories.