[9] **viXra:1305.0183 [pdf]**
*submitted on 2013-05-30 00:59:35*

**Authors:** S.Kalimuthu

**Comments:** 6 Pages. This is a new attempt in set theory 7 geometry

The sum of the interior angles of a number triangles were transformed into linear algebraic equations. The analysis of these equations without assuming the fifth Euclidean postulate established the following theorem: There exists a triangle whose interior angle sum is equal to two right angles

**Category:** Algebra

[8] **viXra:1305.0182 [pdf]**
*submitted on 2013-05-30 01:05:03*

**Authors:** S.Kalimuthu

**Comments:** 4 Pages. This is an entirely new approach in algebra & geometry

By the application of abstract algebra the famous unsolved classical problems trisection of an angle,squaring the circle , duplicating the cube and drawing a regular septagon were shown not possible to solve.. On the other hand,in this work, the application of classical algebra proposed a proposition for the origin of a new field of geometry.

**Category:** Algebra

[7] **viXra:1305.0181 [pdf]**
*submitted on 2013-05-30 01:11:48*

**Authors:** S.Kalimuthu

**Comments:** 3 Pages. Quo Vadis

By applying the basic operations of number theory and set theory to geometry, a new challenging finding has been obtained

**Category:** Algebra

[6] **viXra:1305.0152 [pdf]**
*submitted on 2013-05-24 09:24:45*

**Authors:** S. Kalimuthu

**Comments:** 8 Pages. This is an extra-ordinary math. article.

After establishing the fundamental physics prizes, Yuri Milner said: “Unlike the Nobel in physics, the Fundamental Physics Prize can be awarded to scientists whose ideas have not yet been verified by experiments, which often occurs decades later. Sometimes a radical new idea “really deserves recognition right away because it expands our understanding of at least what is possible.”. Keeping this mind the author formulated two spherical geometrical theorems which may applied for the studies and probes of fundamental particles, quantum gravity, gravitational waves ,dark matter and dark energy.

**Category:** Algebra

[5] **viXra:1305.0151 [pdf]**
*submitted on 2013-05-24 09:27:04*

**Authors:** S. Kalimuthu

**Comments:** 4 Pages. This is an extra-ordinary math. article.

Miles Mathis has shown the following equivalent propositions to Gödel’s incompleteness theorems: [ http://milesmathis.com/godel.html ]
Theorem 1: In any logical system one can construct statements that are neither true nor false (mathematical variations of the liar’s paradox).
Theorem 2: Therefore no consistent system can be used to prove its own consistency. No proof can be proof of itself. In this work , we attempt to prove the first theorem mention above.
Key words: Gödel’s incompleteness theorems ; Miles Mathis’s proposition

**Category:** Algebra

[4] **viXra:1305.0150 [pdf]**
*submitted on 2013-05-24 09:29:12*

**Authors:** S. Kalimuthu

**Comments:** 2 Pages. This is an extra-ordinary math. article.

The classical Euclidean geometry is widely used in all fields of science, engineering and other art fields. The hyperbolic and elliptic non Euclidean geometries are applied in theoretical physics and cosmology. In this short paper, we have come across an interesting non geometrical phenomenon.

**Category:** Algebra

[3] **viXra:1305.0058 [pdf]**
*submitted on 2013-05-08 14:47:25*

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache

**Comments:** 197 Pages.

Study of algebraic structures using subsets was started by George Boole. After the invention of Boolean algebra, subsets were not used in any algebraic structures.
In this book we develop algebraic structures using subsets of a set, or of a group, or semigroup, or a ring and we get algebraic structures.
Using ring or semiring we get only subset semirings.
BY the method we get an infinite number of non-commutative semirings of finite order. We build subset semivector spaces, and describe and develop interesting properties over them.

**Category:** Algebra

[2] **viXra:1305.0057 [pdf]**
*submitted on 2013-05-08 14:50:08*

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache

**Comments:** 167 Pages.

Use of fuzzy neutrosophic models in the study of social problem or technical problem has become a demand for the day due to the involvement of indeterminacy. For always one is not in the position to say true or false, or assign a fuzzy value to any problem. At times, on is not in the position to commit to any of the three statements. In that situation, neutrosophic lmodels play a vital role.
In this book we introduce several fuzzy neutrosophic models to study social problems.

**Category:** Algebra

[1] **viXra:1305.0045 [pdf]**
*submitted on 2013-05-07 21:51:26*

**Authors:** H. J. Siamwalla, A.S.Muktibodh

**Comments:** 15 Pages.

In this paper, we defined the Smarandache seminormal subgroupoids. We have proved
some results for finding the Smarandache seminormal subgroupoids in Z(n) when n is even
and n is odd.

**Category:** Algebra