On varieties of flat nil-semirings
On varieties of flat nil-semirings
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DOI：
10.1007/s00233-023-10337-2
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发表时间：
2023-01
期刊：
影响因子：
0.7
通讯作者：
Y. N. Wu;X. Z. Zhao;M. Ren
中科院分区：
文献类型：
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作者：
Y. N. Wu;X. Z. Zhao;M. Ren
研究了几种平面零半环，给出了有限平面半环是非有限基的充分条件。作为应用，我们证明了该形式的有限平面零半环是有限基于的，当且仅当w由长度不超过2的字母和单词的立方体组成。此外，我们还证明了有限平面零半环对于若干特殊词的集合是无限基的。这肯定地回答了Jackson等人提出的两个问题（J Algebra 611:211 - 245,2022）。
We study some varieties of flat nil-semirings and provide a sufficient condition for a finite flat semiring to be nonfinitely based. As applications, we show that a finite flat nil-semiring of the formis finitely based if and only ifWconsists of cubes of letters and words of length at most 2. Also, we prove that the finite flat nil-semiringsS(W) are nonfinitely based for some setsWof special words in. This affirmatively answers two problems raised by Jackson et al. (J Algebra 611:211–245, 2022).