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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.08546 |
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| _version_ | 1866915729457020928 |
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| author | Shahzamanian, M. H. |
| author_facet | Shahzamanian, M. H. |
| contents | In this paper, we construct explicit families of transformation monoids whose augmentation submodules are simple and whose associated 0-minimal J-classes have rank greater than two. These examples provide new monoids with simple augmentation submodules and non-complete associated graphs. We also establish a connection between the sandwich matrix of a 0-minimal J-class of rank two and the simplicity of the corresponding augmentation module, yielding a criterion that determines simplicity directly from the rank of this matrix for this class of monoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08546 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simplicity of Augmentation Submodules in Monoids with 0-Minimal Ideals of Rank Greater than Two Shahzamanian, M. H. Representation Theory In this paper, we construct explicit families of transformation monoids whose augmentation submodules are simple and whose associated 0-minimal J-classes have rank greater than two. These examples provide new monoids with simple augmentation submodules and non-complete associated graphs. We also establish a connection between the sandwich matrix of a 0-minimal J-class of rank two and the simplicity of the corresponding augmentation module, yielding a criterion that determines simplicity directly from the rank of this matrix for this class of monoids. |
| title | Simplicity of Augmentation Submodules in Monoids with 0-Minimal Ideals of Rank Greater than Two |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.08546 |