منابع مشابه
Division by zero
For any sufficiently strong theory of arithmetic, the set of Diophantine equations provably unsolvable in the theory is algorithmically undecidable, as a consequence of the MRDP theorem. In contrast, we show decidability of Diophantine equations provably unsolvable in Robinson’s arithmetic Q. The argument hinges on an analysis of a particular class of equations, hitherto unexplored in Diophanti...
متن کاملDivision by zero in non-involutive meadows
Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Thus, the multiplicative inverse operation of a meadow is an involution. In this paper, we study 'non-involutive meadows', i.e. variants of meadows ...
متن کاملDivision by Zero in Common Meadows
Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with a that propagates through all operations of the meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero tha...
متن کاملOn nest modules of matrices over division rings
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
متن کاملZPC Matrices and Zero Cycles
Let H be an m × n real matrix and let Zi be the set of column indices of the zero entries of row i of H. Then the conditions |Zk ∩ ∪k−1 i 1 Zi | ≤ 1 for all k 2 ≤ k ≤ m are called the row Zero Position Conditions ZPCs . If H satisfies the ZPC, then H is said to be a row ZPC matrix. If H satisfies the ZPC, thenH is said to be a column ZPCmatrix. The real matrixH is said to have a zero cycle if H...
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ژورنال
عنوان ژورنال: Advances in Linear Algebra & Matrix Theory
سال: 2016
ISSN: 2165-333X,2165-3348
DOI: 10.4236/alamt.2016.62007