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All Solid Varieties of Semigroups

✍ Scribed by Libor Polák

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
131 KB
Volume
219
Category
Article
ISSN
0021-8693

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✦ Synopsis

A solid variety is a variety in which every identity holds as a hyperidentity, that is, we substitute not only elements for the variables but also term operations for the operational symbols. There are obvious necessary conditions for a variety of semigroups to be solid. We will show here that these conditions are also sufficient.

📜 SIMILAR VOLUMES

All Solid Varieties of Semirings
All Solid Varieties of Semirings
✍ K. Denecke; H. Hounnon 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 110 KB

There are exactly three non-trivial solid varieties of semirings, the variety of all rectangular semirings, the variety V NID of all normal, idempotent, distributive semirings, and the subvariety of V NID which is defined by the additional identity x + y y + x ≈ xy + yx.  2002 Elsevier Science (USA

Minimal Noncryptic e-Varieties of Regula
Minimal Noncryptic e-Varieties of Regular Semigroups
✍ F. Pastijn; M.V. Volkov 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 182 KB

We describe all minimal noncryptic e-varieties of regular semigroups, thus generalising earlier results by Rasin and Reilly that dealt with the completely regular and the inverse cases, respectively. As corollaries, we prove that an e-variety of regular semigroups is cryptic if and only if its inter