A sketch of the lattice of commutative nilpotent semigroup varieties

1982 ◽  
Vol 24 (1) ◽  
pp. 285-317 ◽  
Author(s):  
I. O. Korjakov
Keyword(s):  
Nilpotent Semigroup ◽  
Semigroup Varieties

The pn sequences of semigroup varieties generated by combinatorial 0-simple semigroups

2008 ◽  
Vol 59 (3-4) ◽  
pp. 435-446
Author(s):  
Kamilla Kátai-Urbán ◽  
Csaba Szabó
Keyword(s):  
Pn Sequences ◽  
Semigroup Varieties

JOINS OF INVERSE SEMIGROUP VARIETIES AND BAND VARIETIES

1991 ◽  
Vol 01 (03) ◽  
pp. 371-385 ◽  
Author(s):  
PETER R. JONES ◽  
PETER G. TROTTER
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Lattice Of Varieties ◽  
Orthodox Semigroups ◽  
Semigroup Varieties

The joins in the title are considered within two contexts: (I) the lattice of varieties of regular unary semigroups, and (II) the lattice of e-varieties (or bivarieties) of orthodox semigroups. It is shown that in each case the set of all such joins forms a proper sublattice of the respective join of the variety I of all inverse semigroups and the variety B of all bands; each member V of this sublattice is determined by V ∩ I and V ∩ B. All subvarieties of the join of I with the variety RB of regular bands are so determined. However, there exist uncountably many subvarieties (or sub-bivarieties) of the join I ∨ B, all of which contain I and all of whose bands are regular.

scholarly journals Infinite-dimensional triangularizable algebras

2019 ◽  
Vol 31 (1) ◽  
pp. 19-33
Author(s):  
Zachary Mesyan
Keyword(s):  
Vector Space ◽  
Arbitrary Subset ◽  
Linear Transformations ◽  
Nilpotent Semigroup ◽  
Infinite Dimensional ◽  
Closed Fields ◽  
Algebraically Closed Fields ◽  
Basis Vectors

Abstract Let {\mathrm{End}_{k}(V)} denote the ring of all linear transformations of an arbitrary k-vector space V over a field k. We define {X\subseteq\mathrm{End}_{k}(V)} to be triangularizable if V has a well-ordered basis such that X sends each vector in that basis to the subspace spanned by basis vectors no greater than it. We then show that an arbitrary subset of {\mathrm{End}_{k}(V)} is strictly triangularizable (defined in the obvious way) if and only if it is topologically nilpotent. This generalizes the theorem of Levitzki that every nilpotent semigroup of matrices is triangularizable. We also give a description of the triangularizable subalgebras of {\mathrm{End}_{k}(V)} , which generalizes a theorem of McCoy classifying triangularizable algebras of matrices over algebraically closed fields.

The subvariety lattice of the join of two semigroup varieties

2009 ◽  
Vol 25 (6) ◽  
pp. 971-982 ◽  
Author(s):  
Wen Ting Zhang ◽  
Yan Feng Luo
Keyword(s):  
Subvariety Lattice ◽  
Semigroup Varieties

scholarly journals Identities and quasiidentities in the lattice of overcommutative semigroup varieties

2012 ◽  
Vol 86 (1) ◽  
pp. 202-211
Author(s):  
V. Y. Shaprynski
Keyword(s):  
Semigroup Varieties
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