The finite basis problem for infinite involution semigroups of triangular 2 $$\times $$× 2 matrices
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DOI: 10.1007/s00233-016-9832-7
Abstract: Let $$T_n(\mathbb {F})$$Tn(F) and $$UT_n(\mathbb {F})$$UTn(F) be the semigroups of all upper triangular $$n\times n$$n×n matrices and all upper triangular $$n\times n$$n×n matrices with 0s and/or 1s on the main diagonal over a field $$\mathbb… read more here.
Keywords: times matrices; finite basis; mathbb; involution ... See more keywords
THE FINITE BASIS PROBLEM FOR INVOLUTION SEMIGROUPS OF TRIANGULAR $2\times 2$ MATRICES
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DOI: 10.1017/s0004972719001035
Abstract: Let $T_{n}(\mathbb{F})$ be the semigroup of all upper triangular $n\times n$ matrices over a field $\mathbb{F}$ . Let $UT_{n}(\mathbb{F})$ and $UT_{n}^{\pm 1}(\mathbb{F})$ be subsemigroups of $T_{n}(\mathbb{F})$ , respectively, having $0$ s and/or $1$ s on… read more here.
Keywords: finite basis; triangular times; involution; times matrices ... See more keywords
Simple finite-dimensional algebras without finite basis of identities
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DOI: 10.1134/s0037446617030090
Abstract: In 1993, Shestakov posed a problem of existence of a central simple finite-dimensional algebra over a field of characteristic 0 whose identities cannot be defined by a finite set (Dniester Notebook, Problem 3.103). In 2012,… read more here.
Keywords: simple finite; finite dimensional; basis identities; finite basis ... See more keywords