... B 5 1 Smarandache Loops W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, I... ... A 3 A 4 A 5 2 The picture on the cover represents the lattice of subgroups of the Smarandache loop L 15 (8). The lattice of subgroups of... ... But for the Smarandache concepts one wouldn't have studied the collection of subgroups of a loop. This book can be ordered in a paper bound rep... ...rint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 13... ... reviewed and recommended for publication by: Dr. M. Khoshnevisan, Sharif University of Technology, Tehran, Iran. Dr. J. Dezert, Office National d’... ...n Leclerc, 92320 Chantillon, France. Professor C. Corduneanu, Texas State University, Department of Mathematics, Arlington, Texas 76019, USA. ... ...tor SPA(L) of the loop L. Now we proceed onto another type of loop called Jordan loop. DEFINITION [78]: Let L be a loop. We say L is a Jordan loop... ...7 g 7 g 4 g 1 g 3 g 2 g 6 g 3 e This is easily verified to be a Jordan loop of order 8. DEFINITION [65]: A loop L is said to be strictly... ...is strictly non-right alternative. PROBLEMS: 1. Give an example of a Jordan loop of order 7. 2. Can a strongly pseudo associative loop of order...

...The theory of loops (groups without associativity), though researched by several mathematicians has not found a sound expression, for books, be it research level or otherwise, solely dealing with the properties of loops are absent. This...

...randache Non-associative rings W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, I... ...rint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 13... ... Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 1346, Ann Arb... ...lui Street, 2212 Sacele 3, Jud Brasov, Romania. Dr. Andrei Kelarev, Dept. of Mathematics, Univ. of Tasmania, Hobart, Tasmania 7001, Australia. Dr. A... ...1, Australia. Dr. A. R. T. Solarin, Dept. of Mathematics, Obafemi Awolowo University, (formerly University of Ife), Ile-Ife, Nigeria. ... ...ras 103 4.5 Some new notions on Smarandache Lie algebras 106 4 5. JORDAN ALGEBRAS AND SMARANDACHE JORDAN ALGEBRAS 5.1 Basic properties o... ...RDAN ALGEBRAS AND SMARANDACHE JORDAN ALGEBRAS 5.1 Basic properties of Jordan algebras 109 5.2 Smarandache Jordan algebras and its basic properti... ...gs 120 6.3 Lie algebras and Smarandache Lie algebras 121 6.4 Smarandache Jordan algebras 122 6.5 Other non-associative rings and algebras and ... ...e identities using, the program first designed and implemented at Clemson University about 1990 by [31]. They have studied groupoids satisfying the ...

... a field) together with a loop or a groupoid or a vector space or a linear algebra. The two non-associative well-known algebras viz. Lie algebras and Jordan algebras are mainly built using a vector space over a field satisfying special identities called the Jacobi identity and Jordan identity respectively. Study of these algebras started as early as 1940s. Hence the study ...

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...arandache Bialgebraic Structures W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, I... ...rint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 13... ... Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 1346, Ann Arb... ...er reviewed and recommended for publication by: Dr. Andrei Kelarev, Dept. of Mathematics, Univ. of Tasmania, Hobart, Tasmania 7001, Australia. Dr. M... ...f Tasmania, Hobart, Tasmania 7001, Australia. Dr. M. Khoshnevisan, Sharif University of Technology, Tehran, Iran. Dr. A. R. T. Solarin, Dept. of Mat... ...Tehran, Iran. Dr. A. R. T. Solarin, Dept. of Mathematics, Obafemi Awolowo University, (formerly University of Ife), Ile-Ife, Nigeria. ... ...native identities. 35 We in this book do not study Lie algebras or Jordan algebras as non-associative rings. DEFINITION 1.4.84: Let R be a ... ...-biloop P where P is a Bol biloop. We call a biloop L to be a Smarandache Jordan biloop (S-Jordan biloop) if L has a S-sub-biloop P where P is a Jor... ...not totally in the algebraic flavour. They are built for Lie algebras and Jordan algebras as a moniod object in the category of co-moniod. But as ou...

...The study of bialgebraic structures started very recently. Till date there are no books solely dealing with bistructures. The study of bigroups was carried out in 1994-1996. Further research on bigroups and fuzzy bigroups was published...

... Science to Understand Reality 1. A Hidden World 2. Gravity 3. The Power of a Directed desire 4. Proper Development 5. The sin of Creation and the... ...opment 5. The sin of Creation and the Correction A. The Sin B. The Laws of Correction 6. In the End of Days 7. The Spiritual Gene and the Reshimo... .... The Four Elements that Comprise Us 4. The Right Environment 5. The Law of Equivalence of Attributes 6. The power of thought 7. A Chosen People ... ...re not like the ones we buy in a bookstore, or like the ones we study in University. They are not even like the ones we study from in Yeshivot (Rab... ...ter scientists as well as members of the Kabbalah department at Tel-Aviv University. I think that Kabbalah will adopt a more contemporary and easy... ...eople of Israel out of exile. He brought his people to the border between Jordan and Israel, and from there he could not go on with them because hi...

... What is the source of our personal suffering and the suffering of humanity? The vicious circle of human suffering has been idly turning for thousands of years as if without cause, and with no escape. Is this really so? Today we are learning tha...

...Preface: Part 1: A Science to Understand Reality // 1. A Hidden World // 2. Gravity // 3. The Power of a Directed desire // 4. Proper Development // 5. The sin of Creation and the Correction // A. The Sin // B. The Laws of Correction // 6. In the End of Days // 7. The Spiritual Gene and the Reshimot ......