subdirectly irreducible
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2022 ◽  
Author(s):  
Saeide Zahiri ◽  
Arsham Borumand Saeid

Abstract In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras. Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.AMS Classification: 08A72, 03G25, 03B50, 03C05.



Author(s):  
Mohammad Taheri ◽  
Farhad Khaksar Haghani ◽  
Saeed Rasouli


2021 ◽  
Author(s):  
Stefan Veldsman

A congruence is defined for a matroid. This leads to suitable versions of the algebraic isomorphism theorems for matroids. As an application of the congruence theory for matroids, a version of Birkhoff’s Theorem for matroids is given which shows that every nontrivial matroid is a subdirect product of subdirectly irreducible matroids.



2021 ◽  
Vol 128 (2) ◽  
pp. 105-112
Author(s):  
Eun Hwan Roh




2020 ◽  
Vol 59 (5) ◽  
pp. 582-593
Author(s):  
A. A. Stepanova ◽  
D. O. Ptakhov


2020 ◽  
Vol 59 (5) ◽  
pp. 395-403
Author(s):  
A. A. Stepanova ◽  
D. O. Ptakhov


2020 ◽  
Vol 70 (4) ◽  
pp. 815-820
Author(s):  
Christian Herrmann

AbstractGiven a subdirectly irreducible ∗-regular ring R, we show that R is a homomorphic image of a regular ∗-subring of an ultraproduct of the (simple) eRe, e in the minimal ideal of R; moreover, R (with unit) is directly finite if all eRe are unit-regular. For any subdirect product of artinian ∗-regular rings we construct a unit-regular and ∗-clean extension within its variety.



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