Abstract
This paper is based on a general project concerning semigroup theoretical methods in the study of associative rings. Let A be an associative algebra over a field K. The main idea is to introduce semigroup constructions of certain types that strongly reflect the properties of A. Then the aim is to study the structure of these semigroups and to derive certain invariants of the algebra. Some of the classical constructions that motivate our approach include: the lattice of left ideals of A and the set of orbits on A under the action of certain groups derived from the unit group U(A) of A. The focus is on the case of finite dimensional algebras over an algebraically closed field.
To Mohan and Lex on the occasion of their anniversaries
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This work was supported by MNiSW research grant N201 420539.
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Okniński, J. (2014). On Certain Semigroups Derived from Associative Algebras. In: Can, M., Li, Z., Steinberg, B., Wang, Q. (eds) Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics. Fields Institute Communications, vol 71. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0938-4_10
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DOI: https://doi.org/10.1007/978-1-4939-0938-4_10
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