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[4] viXra:2408.0102 [pdf] submitted on 2024-08-26 02:03:49
Authors: Miloš Čojanović
Comments: 5 Pages.
A cubic equation is solvable by radicals. This means that the solutions of the cubic equation can be obtained using four basic arithmetic operations which include addition, subtraction, multiplication and division, and taking the square and cube roots.
Category: Algebra
[3] viXra:2408.0098 [pdf] submitted on 2024-08-24 07:11:01
Authors: Huanyin Chen, Dayong Liu
Comments: 24 Pages.
We provide representations for the group inverse and generalized group inverse of an anti-triangular operator matrix of the form$left(begin{array}{cc}a&bc&0end{array}ight)$ under the conditions $ca=c$ or $ab=b$. Specifically, we present the weak group inverse for these types of anti-triangular block operator matrices.
Category: Algebra
[2] viXra:2408.0066 [pdf] submitted on 2024-08-16 20:49:52
Authors: Xiaochun Mei
Comments: 2 Pages. In Chinese
In this paper, the Fermat equation is written in the form of quadratic indeterminate equation, and its solutions are compared with the Pythagorean numbers of quadratic equation. It is proved in a very simple method that the Fermat equation has no integer solutions in case of p>2.
Category: Algebra
[1] viXra:2408.0039 [pdf] submitted on 2024-08-09 14:40:54
Authors: Huanyin Chen
Comments: 18 Pages.
We derive the generalized group inverse of a triangular block matrix over a Banach algebra. We apply this formula in order to find the generalized group inverse of $2times 2$ block operators under some conditions. In particular, the weak group inverse of certain block operator matricesare given.
Category: Algebra
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