Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings

Extension of Endomorphisms of the Subsemigroup GE 2 + (R) to Endomorphisms of GE 2 + (R[x]), Where R is a Partially-Ordered Commutative Ring Without Zero Divisors

“…Assume the contrary. Let A = 2 + 2x + 3x 2 + 3x 3 + 3x 4 + 2x 5 + 2x 6 + x 7 1 + 2x + 3x 2 + 2x 3 + 2x 4 + x 5 1 + 2x + 2x 2 + 2x 3 + 2x 4 + 2x 5 + x 6 + x 7 1 + x + 2x 2 + 2x 3 + x 4 + x 5…”

“…In [4], E. I. Bunina and P. P. Semenov described the automorphisms of the subsemigroup of the invertible nonnegative matrices of order at least 2 over commutative partially-ordered rings with 1/2. In [5], the same authors found necessary and sufficient conditions for the elementary equivalence of such semigroups. In [1], Bunina described the automorphisms of the semigroup G 2 (R), where R is a partially ordered commutative ring with 1/2 that is generated by its invertible elements.…”

Endomorphisms of the Semigroup G2(r) Over Partially Ordered Commutative Rings Without Zero Divisors and with 1/2

“…In [3], E. I. Bunina and A. V. Mikhalev described necessary and sufficient conditions for semigroups considered in [2] to be elementarily equivalent. In [4], E. I. Bunina and P. P. Semenov described automorphisms of G n (R) in the case of commutative partially ordered rings R with 1/2, and in [5] the same authors found necessary and sufficient conditions for semigroups considered above to be elementarily equivalent. In [1], E. I. Bunina described automorphisms of G 2 (R) in the case of a partially ordered ring R with 1/2 generated by its invertible elements.…”

Автоморфизмы Полугрупп Обратимых Матриц С Неотрицательными Целыми Элементами

“…В работе [3] Е. И. Бунина и А. В. Михалёв нашли необходимые и достаточные условия для того, чтобы эти полугруппы были элементарно эквивалентны. В работе [4] Е. И. Бунина и П. П. Семёнов описали автоморфизмы полугруппы обратимых неотрицательных матриц порядка > 2 над коммутативными частично упорядоченными кольцами с обратимой двойкой, а в работе [5] нашли необходимые и достаточные условия для их элементарной эквивалентности. Во всех работах [2]- [5] было существенно, что в кольце R обратима двойка либо хотя бы какое-то целое число > 1.…”