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Norms on semirings. I.

Vítězslav Kala, Tomáš Kepka, Petr Němec (2010)

Acta Universitatis Carolinae. Mathematica et Physica

Note on strongly nil clean elements in rings

Aleksandra Kostić, Zoran Z. Petrović, Zoran S. Pucanović, Maja Roslavcev (2019)

Czechoslovak Mathematical Journal

Let R be an associative unital ring and let a R be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.

Notes on commutative parasemifields

Vítězslav Kala, Tomáš Kepka, Miroslav Korbelář (2009)

Commentationes Mathematicae Universitatis Carolinae

Parasemifields (i.e., commutative semirings whose multiplicative semigroups are groups) are considered in more detail. We show that if a parasemifield S contains + as a subparasemifield and is generated by + { a } , a S , as a semiring, then S is (as a semiring) not finitely generated.

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